Edit: Sorry, I was unclear, it is an official branch and not just a personal fork.
Some links: http://msujaws.wordpress.com/2012/03/15/mozillas-ux-nightly-... https://wiki.mozilla.org/UX_Branch
Nope, Aurora is something else. It's the build after Nightly. Nightly includes pre-alpha releases, Aurora includes alpha releases.
You are however correct that Nightly and Nightly UX are not the same thing. Although if I'm not mistaken the only difference between two of them is that Nightly UX also gets pre-alpha UI changes as well as under the hood changes that Nightly normally gets (almost daily). It's a bit confusing.
To sum it up, the release cycle goes like this:
Nightly (pre-alpha) > Aurora (alpha) > Firefox Beta (beta) > Firefox (stable)
In any case, you can just install it and experience it yourself. If you're like me who started using Chrome because you were sick of how slow and unstable Firefox was, you'll be amazed how good it is now.