What's the difference between X, Xorg, Xserver, etc. and their respective versions?

I don't understand the difference between X, Xorg, Xserver, etc etc... and what most specifically confuses me is this:

It seems I'm running X.Org X Server 1.7.7, which is apparently the newest version. Yet I also see references all over the web to X Server 1.11 and 1.12 (only 1.11 supports AMD Catalyst, which is my issue).

So, I am guessing that the 1.11 refers to something that runs on top of whatever is at version 1.7.7? What is the difference, and how can I ensure that I am running version 1.11 (of whatever it actually is) instead of 1.12?

This isn't layering or anything more complex - you're just running an old version. The X.Org X server (aka Xorg) from the upstream project is up to 1.13.1 now, with 1.7.7 being a several year old release. Perhaps 1.7.7 was the last packaged for whatever distro/package branch you're on?