.NET Core vs Mono

What is the difference between .NET Core and Mono?

I found a statement on the official site that said: "Code written for it is also portable across application stacks, such as Mono."

My goal is to use C#, LINQ, EF7 and Visual Studio to create a website that can be ran/hosted on Linux.

Someone told me that he wanted it to be "in Mono", but I don't know what that means. I know I want to use the .NET Core 1.0 with the technologies I listed above. He also said he wanted to use "fast CGI". I don't know what that means either.

Can you help me make sense of all these terms and if my expectations are realistic?

Necromancing.
Providing an actual answer.

What is the difference between .Net Core and Mono?

.NET Core now officially is the future of .NET. It started for most part with a re-write of the ASP.NET MVC framework and console applications, which of course includes server applications. (Since it's Turing-complete and supports interop with C dlls, you could, if you absolutely wanted to, also write your own desktop applications with it, for example through 3rd-party libraries like Avalonia, which were a bit very basic at the time I first wrote this, which meant you were pretty much limited to web or server stuff.) Over time, many APIs have been added to .NET Core, so much so that after version 3.1, .NET Core will jump to version 5.0, be known as .NET 5.0 without the "Core", and that then will be the future of the .NET Framework. What used to be the full .NET Framework will linger around in maintenance mode as Full .NET Framework 4.8.x for a few decades, until it will die (maybe there are still going to be some upgrades, but I doubt it). In other words, .NET Core is the future of .NET, and Full .NET Framework will go the way of the Dodo/Silverlight/WindowsPhone.

The main point of .NET Core, apart from multi-platform support, is to improve performance, and to enable "native compilation"/self-contained-deployment (so you don't need .NET framework/VM installed on the target machine.
On the one hand, this means docker.io support on Linux, and on the other, self-contained deployment is useful in "cloud-computing", since then you can just use whatever version of the dotnet-CORE framework you like, and you don't have to worry about which version(s) of the .NET framework the sysadmin has actually installed.

While the .NET Core runtime supports multiple operating systems and processors, the SDK is a different story. And while the SDK supports multiple OS, ARM support for the SDK is/was still work in progress. .NET Core is supported by Microsoft. Dotnet-Core did not come with WinForms or WPF or anything like that.

• As of version 3.0, WinForms and WPF is also supported by .NET Core, but only on Windows, and only by C#. Not by VB.NET (VB.NET support planned for v5 in 2020). And there is no Forms Designer in .NET Core: it's being shipped with a Visual Studio update later, at an unspecified time.
• WebForms are still not supported by .NET Core, and there are no plans to support them, ever (Blazor is the new kid in town for that).
• .NET Core also comes with System.Runtime, which replaces mscorelib.
• Oftentimes, .NET Core is mixed up with NetStandard, which is a bit of a wrapper around System.Runtime/mscorelib (and some others), that allows you to write libraries that target .NET Core, Full .NET Framework and Xamarin (iOS/Android), all at the same time.
• the .NET Core SDK does not/did not work on ARM, at least not last time I checked.

"The Mono Project" is much older than .NET Core.
Mono is Spanish and means Monkey, and as a side-remark, the name has nothing to do with mononucleosis (hint: you could get a list of staff under http://primates.ximian.com/).
Mono was started in 2005 by Miguel de Icaza (the guy that started GNOME - and a few others) as an implementation of the .NET Framework for Linux (Ximian/SuSe/Novell). Mono includes Web-Forms, Winforms, MVC, Olive, and an IDE called MonoDevelop (also knows as Xamarin Studio or Visual Studio Mac). Basically the equivalent of (OpenJDK) JVM and (OpenJDK) JDK/JRE (as opposed to SUN/Oracle JDK). You can use it to get ASP.NET-WebForms + WinForms + ASP.NET-MVC applications to work on Linux.

Mono is supported by Xamarin (the new company name of what used to be Ximian, when they focused on the Mobile market, instead of the Linux market), and not by Microsoft.
(since Xamarin was bought by Microsoft, that's technically [but not culturally] Microsoft.)
You will usually get your C# stuff to compile on mono, but not the VB.NET stuff.
Mono misses some advanced features, like WSE/WCF and WebParts.
Many of the Mono implementations are incomplete (e.g. throw NotImplementedException in ECDSA encryption), buggy (e.g. ODBC/ADO.NET with Firebird), behave differently than on .NET (for example XML-serialization) or otherwise unstable (ASP.NET MVC) and unacceptably slow (Regex). On the upside, the Mono toolchain also works on ARM.

As far as .NET Core is concerned, when they say cross-platform, don't expect that cross-platform means that you could actually just apt-get install .NET Core on ARM-Linux, like you can with ElasticSearch. You'll have to compile the entire framework from source.
That is, if you have that space (e.g. on a Chromebook, which has a 16 to 32 GB total HD).
It also used to have issues of incompatibility with OpenSSL 1.1 and libcurl.
Those have been rectified in the latest version of .NET Core Version 2.2.
So much for cross-platform.

I found a statement on the official site that said, "Code written for it is also portable across application stacks, such as Mono".

As long as that code doesn't rely on WinAPI-calls, Windows-dll-pinvokes, COM-Components, a case-insensitive file system, the default-system-encoding (codepage) and doesn't have directory separator issues, that's correct. However, .NET Core code runs on .NET Core, and not on Mono. So mixing the two will be difficult. And since Mono is quite unstable and slow (for web applications), I wouldn't recommend it anyway. Try image-processing on .NET core, e.g. WebP or moving GIF or multipage-tiff or writing text on an image, you'll be nastily surprised.

Note:
As of .NET Core 2.0, there is System.Drawing.Common (NuGet), which contains most of the functionality of System.Drawing. It should be more or less feature-complete in .NET-Core 2.1. However, System.Drawing.Common uses GDI+, and therefore won't work on Azure (System.Drawing libraries are available in Azure Cloud Service [basically just a VM], but not in Azure Web App [basically shared hosting?])
So far, System.Drawing.Common works fine on Linux/Mac, but has issues on iOS/Android - if it works at all, there.
Prior to .NET Core 2.0, that is to say sometime mid-February 2017, you could use SkiaSharp for imaging (example) (you still can).
Post .net-core 2.0, you'll notice that SixLabors ImageSharp is the way to go, since System.Drawing is not necessarely secure, and has a lot of potential or real memory leaks, which is why you shouldn't use GDI in web-applications; Note that SkiaSharp is a lot faster than ImageSharp, because it uses native-libraries (which can also be a drawback). Also, note that while GDI+ works on Linux & Mac, that doesn't mean it works on iOS/Android.

Code not written for .NET (non-Core) is not portable to .NET Core.
Meaning, if you want a non-GPL C# library like PDFSharp to create PDF-documents (very commonplace), you're out of luck (at the moment) (not anymore). Never mind ReportViewer control, which uses Windows-pInvokes (to encrypt, create mcdf documents via COM, and to get font, character, kerning, font embedding information, measure strings and do line-breaking, and for actually drawing tiffs of acceptable quality), and doesn't even run on Mono on Linux
(I'm working on that).

Also, code written in .NET Core is not portable to Mono, because Mono lacks the .NET Core runtime libraries (so far).

My goal is to use C#, LINQ, EF7, visual studio to create a website that can be ran/hosted in linux.

EF in any version that I tried so far was so goddamn slow (even on such simple things like one table with one left-join), I wouldn't recommend it ever - not on Windows either.
I would particularly not recommend EF if you have a database with unique-constrains, or varbinary/filestream/hierarchyid columns. (Not for schema-update either.)
And also not in a situation where DB-performance is critical (say 10+ to 100+ concurrent users).
Also, running a website/web-application on Linux will sooner or later mean you'll have to debug it.
There is no debugging support for .NET Core on Linux. (Not anymore, but requires JetBrains Rider.)
MonoDevelop does not (yet) support debugging .NET Core projects.
If you have problems, you're on your own. You'll have to use extensive logging.
Be careful, be advised extensive logging will fill your disk in no time, particularly if your program enters an infinite loop or recursion.
This is especially dangerous if your web-app runs as root, because log-in requires logfile-space - if there's no free space left, you won't be able to login anymore.
(Normally, about 5% of diskspace is reserved for user root [aka administrator on Windows], so at least the administrator can still log in if the disk is almost full. But if your applications run as root, that restriction does not apply for their disk usage, and so their logfiles can use 100% of the remaining free space, so not even the administrator can log in any more.)
It's therefore better not to encrypt that disk, that is, if you value your data/system.

Someone told me that he wanted it to be "in Mono", but I don't know what that means.

It either means he doesn't want to use .NET Core, or he just wants to use C# on Linux/Mac. My guess is he just wants to use C# for a Web-App on Linux. .NET Core is the way to go for that, if you absolutely want to do it in C#. Don't go with "Mono proper"; on the surface, it would seem to work at first - but believe me you will regret it because Mono's ASP.NET MVC isn't stable when your server runs long-term (longer than 1 day) - you have now been warned. See also the "did not complete" references when measuring Mono performance on the techempower benchmarks.

I know I want to use the .Net Core 1.0 framework with the technologies I listed above. He also said he wanted to use "fast cgi". I don't know what that means either.

It means he wants to use a high-performance full-featured WebServer like nginx (Engine-X), possibly Apache.
Then he can run mono/dotnetCore with virtual name based hosting (multiple domain names on the same IP) and/or load-balancing. He can also run other websites with other technologies, without requiring a different port-number on the web-server. It means your website runs on a fastcgi-server, and nginx forwards all web-requests for a certain domain via the fastcgi-protocol to that server. It also means your website runs in a fastcgi-pipeline, and you have to be careful what you do, e.g. you can't use HTTP 1.1 when transmitting files.
Otherwise, files will be garbled at the destination.
See also here and here.

To conclude:
.NET Core at present (2016-09-28) is not really portable, nor is is really cross-platform (in particular the debug-tools).
Nor is native-compilation easy, especially for ARM.
And to me, it also does not look like its development is "really finished", yet.
For example, System.Data.DataTable/DataAdaper.Update is missing... (not anymore with .NET Core 2.0)
Together with the System.Data.Common.IDB* interfaces. (not anymore with .NET Core 1.1)
if there ever was one class that is often used, DataTable/DataAdapter would be it...
Also, the Linux-installer (.deb) fails, at least on my machine, and I'm sure I'm not the only one that has that problem.
Debug, maybe with Visual Studio Code, if you can build it on ARM (I managed to do that - do NOT follow Scott Hanselman's blog-post if you do that - there's a howto in the wiki of VS-Code on github), because they don't offer the executable.
Yeoman also fails. (I guess it has something to do with the nodejs version you installed - VS Code requires one version, Yeoman another... but it should run on the same computer. pretty lame
Never mind that it should run on the node version shipped by default on the OS.
Never mind that there should be no dependency on NodeJS in the first place.
The kestell server is also work in progress.
And judging by my experience with the mono-project, I highly doubt they ever tested .NET Core on FastCGI, or that they have any idea what FastCGI-support means for their framework, let alone that they tested it to make sure "everything works". In fact, I just tried making a fastcgi-application with .NET Core and just realized there is no FastCGI library for .NET Core "RTM"...

So when you're going to run .NET Core "RTM" behind nginx, you can only do it by proxying requests to kestrell (that semi-finished nodeJS-derived web-server) - there's no fastcgi support at present in .NET Core "RTM", AFAIK. Since there is no .net core fastcgi library, and no samples, it's also highly unlikely that anybody did any testing on the framework to make sure fastcgi works as expected.

I also question the performance.
In the (preliminary) techempower-benchmark (round 13), aspnetcore-linux ranks on 25% relative to the best performance, while comparable frameworks like Go (golang) rank at 96.9% of peak performance (and that is when returning plaintext without file-system access only). .NET Core does a little better on JSON-serialization, but it does not look compelling either (go reaches 98.5% of peak, .NET core 65%). That said, it can't possibly be worse than "mono proper".

Also, since it's still relatively new, not all of the major libraries have been ported (yet), and I doubt that some of them will ever be ported.
Imaging support is also questionable at best.
For anything encryption, use BouncyCastle instead.

Can you help me make sense of all these terms and if my expectations are realistic?

I hope i helped you making more sense with all these terms.
As far as your expecations go:
Developing a Linux application without knowing anything about Linux is a really stupid idea in the first place, and it's also bound to fail in some horrible way one way or the other. That said, because Linux comes at no licensing costs, it's a good idea in principle, BUT ONLY IF YOU KNOW WHAT YOU DO.
Developing an application for a platform where you can't debug your application on is another really bad idea.
Developing for fastcgi without knowing what consequences there are is yet another really bad idea.

Doing all these things on a "experimental" platform without any knowledge of that platform's specifics and without debugging support is suicide, if your project is more than just a personal homepage. On the other hand, I guess doing it with your personal homepage for learning purposes would probably be a very good experience - then you get to know what the framework and what the non-framework problems are.
You can for example (programmatically) loop-mount a case-insensitive fat32, hfs or JFS for your application, to get around the case-sensitivity issues (loop-mount not recommended in production).

To summarize
At present (2016-09-28), I would stay away from .NET Core (for production usage). Maybe in one to two years, you can take another look, but probably not before.
If you have a new web-project that you develop, start it in .NET Core, not mono.

If you want a framework that works on Linux (x86/AMD64/ARMhf) and Windows and Mac, that has no dependencies, i.e. only static linking and no dependency on .NET, Java or Windows, use Golang instead. It's more mature, and its performance is proven (Baidu uses it with 1 million concurrent users), and golang has a significantly lower memory footprint. Also golang is in the repositories, the .deb installs without problems, the sourcecode compiles - without requiring changes - and golang (in the meantime) has debugging support with delve and JetBrains Gogland on Linux (and Windows and Mac). Golang's build process (and runtime) also doesn't depend on NodeJS, which is yet another plus.

As far as mono goes, stay away from it.
It is nothing short of amazing how far mono has come, but unfortunately that's no substitute for its performance/scalability and stability issues for production applications.
Also, mono-development is quite dead, they largely only develop the parts relevant to Android and iOS anymore, because that's where Xamarin makes their money.
Don't expect Web-Development to be a first-class Xamarin/mono citizen.
.NET Core might be worth it, if you start a new project, but for existing large web-forms projects, porting over is largely out of the question, the changes required are huge. If you have a MVC-project, the amount of changes might be manageable, if your original application design was sane, which is mostly not the case for most existing so-called "historically grown" applications.

December 2016 Update:
Native compilation has been removed from .NET Core preview, as it is not yet ready...

Seems like they have improved pretty heavily on the raw text-file benchmark, but on the other hand, it's gotten pretty buggy. Also, it further deteriorated in the JSON benchmarks. Curious also that entity framework shall be faster for updates than Dapper - although both at record slowness. This is very unlikely to be true. Looks like there still are more than just a few bugs to hunt.

Also, there seems to be relief coming on the Linux IDE front.
JetBrains released "Project Rider", an early access preview of a C#/.NET Core IDE for Linux (and Mac and Windows), that can handle Visual Studio Project files. Finally a C# IDE that is usable & that isn't slow as hell.

Conclusion: .NET Core still is pre-release quality software as we march into 2017. Port your libraries, but stay away from it for production usage, until framework quality stabilizes.
And keep an eye on Project Rider.

2017 Update
Have migrated my (brother's) homepage to .NET Core for now.
So far, the runtime on Linux seems to be stable enough (at least for small projects) - it survived a load test with ease - mono never did.
Also, it looks like I mixed up .NET-Core-native and .NET-Core-self-contained-deployment. Self-contained deployment works, but it is a bit underdocumented, although it's super easy (the build/publish tools are a bit unstable, yet - if you encounter "Positive number required. - Build FAILED." - run the same command again, and it works).

You can run

dotnet restore -r win81-x64
dotnet build -r win81-x64
dotnet publish -f netcoreapp1.1 -c Release -r win81-x64

Note: As per .NET Core 3, you can publish everything minified as a single file:

dotnet publish -r win-x64 -c Release /p:PublishSingleFile=true
dotnet publish -r linux-x64 -c Release /p:PublishSingleFile=true

However, unlike go, it's not a statically linked executable, but a self-extracting zip file, so when deploying, you might run into problems, especially if the temp directory is locked down by group policy, or some other issues. Works fine for a hello-world program, though. And if you don't minify, the executable size will clock in at something around 100 MB.

And you get a self-contained .exe-file (in the publish directory), which you can move to a Windows 8.1 machine without .NET framework installed and let it run. Nice. It's here that dotNET-Core just starts to get interesting. (mind the gaps, SkiaSharp doesn't work on Windows 8.1 / Windows Server 2012 R2, [yet] - the ecosystem has to catch up first - but interestingly, the Skia-dll-load-fail doesn't crash the entire server/application - so everything else works)

(Note: SkiaSharp on Windows 8.1 is missing the appropriate VC runtime files - msvcp140.dll and vcruntime140.dll. Copy them into the publish-directory, and Skia will work on Windows 8.1.)

August 2017 Update
.NET Core 2.0 released.
Be careful - comes with (huge breaking) changes in authentication...
On the upside, it brought the DataTable/DataAdaper/DataSet classes back, and many more.
Realized .NET Core is still missing support for Apache SparkSQL, because Mobius isn't yet ported. That's bad, because that means no SparkSQL support for my IoT Cassandra Cluster, so no joins...
Experimental ARM support (runtime only, not SDK - too bad for devwork on my Chromebook - looking forward to 2.1 or 3.0).
PdfSharp is now experimentally ported to .NET Core.
JetBrains Rider left EAP. You can now use it to develop & debug .NET Core on Linux - though so far only .NET Core 1.1 until the update for .NET Core 2.0 support goes live.

May 2018 Update
.NET Core 2.1 release imminent. Maybe this will fix NTLM-authentication on Linux (NTLM authentication doesn't work on Linux {and possibly Mac} in .NET-Core 2.0 with multiple authenticate headers, such as negotiate, commonly sent with ms-exchange, and they're apparently only fixing it in v2.1, no bugfix release for 2.0).
But I'm not installing preview releases on my machine. So waiting.
v2.1 is also said to greatly reduce compile times. That would be good.

Also, note that on Linux, .NET Core is 64-Bit only !
There is no, and there will be no, x86-32 version of .NET Core on Linux.
And the ARM port is ARM-32 only. No ARM-64, yet.
And on ARM, you (at present) only have the runtime, not the dotnet-SDK.

And one more thing:
Because .NET-Core uses OpenSSL 1.0, .NET Core on Linux doesn't run on Arch Linux, and by derivation not on Manjaro (the most popular Linux distro by far at this point in time), because Arch Linux uses OpenSSL 1.1. So if you're using Arch Linux, you're out of luck (with Gentoo, too).

Edit:

Latest version of .NET Core 2.2+ supports OpenSSL 1.1. So you can use it on Arch or (k)Ubuntu 19.04+. You might have to use the .NET-Core install script though, because there are no packages, yet.

On the upside, performance has definitely improved:

.NET Core 3:
.NET-Core v 3.0 is said to bring WinForms and WPF to .NET-Core.
However, while WinForms and WPF will be .NET Core, WinForms and WPF in .NET-Core will run on Windows only, because WinForms/WPF will use the Windows-API.

Note:
.NET Core 3.0 is now out (RTM), and there is WinForms and WPF support, but only for C# (on Windows). There is no WinForms-Core-Designer. The designer will, eventually, come with a Visual Studio update, somewhen. WinForms support for VB.NET is not supported, but is planned for .NET 5.0 somewhen in 2020.

PS:

echo "DOTNET_CLI_TELEMETRY_OPTOUT=1" >> /etc/environment
export DOTNET_CLI_TELEMETRY_OPTOUT=1 

If you've used it on windows, you probably never saw this:

The .NET Core tools collect usage data in order to improve your experience.
The data is anonymous and does not include command-line arguments.
The data is collected by Microsoft and shared with the community.
You can opt out of telemetry by setting a DOTNET_CLI_TELEMETRY_OPTOUT environment variable to 1 using your favorite shell.
You can read more about .NET Core tools telemetry @ https://aka.ms/dotnet-cli-telemetry.

I thought I'd mention that I think monodevelop (aka Xamarin Studio, the Mono IDE, or Visual Studio Mac as it is now called on Mac) has evolved quite nicely, and is - in the meantime - largely usable.
However, JetBrains Rider (2018 EAP at this point in time) is definitely a lot nicer and more reliable (and the included decompiler is a life-safer), that is to say, if you develop .NET-Core on Linux or Mac. MonoDevelop does not support Debug-StepThrough on Linux in .NET Core, though, since MS does not license their debugging API dll (except for VisualStudio Mac ... ). However, you can use the Samsung debugger for .NET Core through the .NET Core debugger extension for Samsung Debugger for MonoDevelop

Disclaimer:
I don't use Mac, so I can't say if what I wrote here applies to FreeBSD-Unix based Mac as well. I am refering to the Linux (Debian/Ubuntu/Mint) version of JetBrains Rider, mono, MonoDevelop/VisualStudioMac/XamarinStudio and .NET-Core. Also, Apple is contemplating a move from Intel-processors to self-manufactured ARM(ARM-64?)-based processors, so much of what applies to Mac right now might not apply to Mac in the future (2020+).

Also, when I write "mono is quite unstable and slow", the unstable relates to WinFroms & WebForms applications, specifically executing web-applications via fastcgi or with XSP (on the 4.x version of mono), as well as XML-serialization-handling peculiarities, and the quite-slow relates to WinForms, and regular expressions in particular (ASP.NET-MVC uses regular expressions for routing as well).

When I write about my experience about mono 2.x, 3.x and 4.x, that also does not necessarely mean these issues haven't been resolved by now, or by the time you are reading this, nor that if they are fixed now, that there can't be a regression later that reintroduces any of these bugs/features. Nor does that mean that if you embed the mono-runtime, you'll get the same results as when you use the (dev) system's mono runtime. It also doesn't mean that embedding the mono-runtime (anywhere) is necessarely free.

All that doesn't necessarely mean mono is ill-suited for iOS or Android, or that it has the same issues there. I don't use mono on Android or IOS, so I'm in no positon to say anything about stability, usability, costs and performance on these platforms. Obviously, if you use .NET on Android, you have some other costs considerations to do as well, such as weighting xamarin-costs vs. costs and time for porting existing code to Java. One hears mono on Android and IOS shall be quite good. Take it with a grain of salt. For one, don't expect the default-system-encoding to be the same on android/ios vs. Windows, and don't expect the android filesystem to be case-insensitive, and don't expect any windows fonts to be present.

In the .NET world there are two types of CLRs, "full" CLRs and Core CLRs, and these are quite different things.

There are two "full" CLR implementations, the Microsoft native .NET CLR (for Windows) and the Mono CLR (which itself has implementations for Windows, linux and unix (Mac OS X and FreeBSD)). A full CLR is exactly that - everything, pretty much, that you need. As such, "full" CLRs tend to be large in size.

Core CLRs are on the other hand are cut down, and much smaller. Because they are only a core implementation, they are unlikely to have everything you need in them, so with Core CLRs you add feature sets to the CLR that your specific software product uses, using NuGet. There are Core CLR implementations for Windows, linux (various) and unix (Mac OS X and FreeBSD) in the mix. Microsoft have or are refactoring the .NET framework libraries for Core CLR too, to make them more portable for the core context. Given mono's presence on *nix OSs it would be a surprise if the Core CLRs for *nix did not include some mono code base, but only the Mono community and Microsoft could tell us that for sure.

Also, I'd concur with Nico in that Core CLRs are new -- it's at RC2 at the moment I think. I wouldn't depend on it for production code yet.

To answer your question you could delivery your site on linux using Core CLR or Mono, and these are two different ways of doing it. If you want a safe bet right now I'd go with mono on linux, then port if you want to later, to Core.