Can someone clarify Ubuntu (Debian) dist-upgrade for me?

The command apt-get upgrade will not add or remove packages. apt-get dist-upgrade will add or remove packages as required.

The command apt-get dist-upgrade will not automatically upgrade you from one release to another unless you have also updated your sources (/etc/apt/sources.list) to point at a newer release.

man apt-get

upgrade
    upgrade is used to install the newest versions of all packages 
    currently installed on the system from the sources enumerated 
    in /etc/apt/sources.list.

dist-upgrade
    dist-upgrade, in addition to performing the function of upgrade, 
    also intelligently handles changing dependencies with new versions 
    of packages;

Are there special concerns to be aware of when doing a dist-upgrade vs upgrade?

For the most part I always apt-get dist-upgrade to apply updates to a system. Of course pay attention to exactly what new packages are being added or removed. Frequently this happens when something is being added like a newer kernel that isn't compatible with the previous and you will have to recompile modules. If you have some kernel module you had to build on your own, then you may need to make sure you recompile it for the new kernel. I have a couple systems with network interfaces not supported by the stock kernel that I have to recompile the network driver after each kernel update.

upgrade vs. dist-upgrade are really debian terms. In debian you'd use upgrade to get changes within a stable release (which would not involve anything so drastic as a removal) and dist-upgrade to go between releases. dist-upgrade should have the same results as upgrade assuming no removals are necessary.

Going between releases would require changing your sources.list to point at the new release.

Ubuntu does not have the same ultraconservative release model, so the terms do not map cleanly -- you'd generally just want to use dist-upgrade unless you're going between releases, in which case you use its own upgrader, do-release-upgrade.