It was, at the time of the Unix wars, a rather childish way of 'protesting' the use of trademarks on the name 'UNIX' by AT&T, Novell, SCO etc. in their fights against other Unixy OS vendors. There were urban legends going around on IRC and Usenet that those companies would sue everybody using the word 'Unix' but not using the full name would absolve you of that responsibility. Legally this in the class of 'cops can't lie to you when you ask them if they're a cop' and 'free men doctrine' and such but it was wide spread at the time.
The irony is of course that Unix-like OS vendors spend so much time fighting each other that it was basically mutually assured destruction, and proprietary Unix systems went the way of the dinosaur after the dot com crash.
I tend to use *nix for things that are UNIX-like. I think of un*x in the older sense from the other parent "it's not actually UNIX and f*ck the trademark" but I'm not sure that dichotomy in my mind is useful anymore.
