Do I have to download both the 14.04 and the 14.04.1 versions of ubuntu?

In the release page of Ubuntu, I see that both the 14.04.1 and the 14.04 versions are offered for download. Do I need them both? That is, is 14.04 a prerequisite for installing 14.04.1? Or can I just download the last version ubuntu-14.04.1-desktop-amd64.iso?

No, just download 14.04.1 It has lots of good bug fixes, like bug 1309458, it fixes the ubiquity installer crashing when clicking release notes, and bug 1315866 with the usb creator, it's a workaround for Python Qt4 being sucky.

You can see the full list of changes here.

It is different to the Windows 8 + 8.1 system, in that this was planned to be "public". Normally, windows just give their releases "secretly", without revealing they are upgrading to what is called a "point release".

14.04.1 hasn't really got any new features, it just comes with all the updates you have to do if you download 14.04 included.

So for clarification, you can either download 14.04 + lots of updates, or just 14.04.1. It has them all included already. 14.04 won't have the bugs, but 14.04 is more work to get patched. ^{_{Kudos @CharlesGreen}}

When 14.04 is fully updated it identifies as 14.04.1 - they are identical. So I installed 14.04, and when I run

lsb_release -a

I get some irrelevant details (for this example) and then:

...
Distributor ID: Ubuntu
Description:    Ubuntu 14.04.1 LTS
Release:    14.04
Codename:   trusty

So you can see that the Descriptor is 14.04.1 LTS, even though I installed 14.04 (when it was first released).

My pronouns are He / Him

The ".1" is simply 14.04 with all updates up until the start of August 2014 already rolled into it.

You can download and install 14.04 and bring it up to date with updates and it will then start showing itself as "14.04.1", so the 14.04.1 ISO simply saves you about 300MB worth of updates being downloaded after initial installation.

As time goes on, the ".2" version will be released and so forth. So far most LTS releases have had four point releases in their lifetimes.

You can find out if you're on 14.04.1 already by issuing the lsb_release -a command in a terminal. You'll see something like this:

$ lsb_release -a
No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 14.04.1 LTS
Release:    14.04
Codename:   trusty

The description shows that we are running the .1 release of 14.04.