I think the difference was that George Lucas was just good natured about it
Yeah, that's another one of the differences. But I think that's minor (and really not even relevant at this point) compared to the other differences, and I think one of the main differences is what I mentioned upthread: Star Wars fans aren't making Star Wars fanfilms as a kind of a "watch this instead of what the studio is actually putting out," whereas a fair amount of Star Trek fanfilms (and Axanar especially) had that air about them. Basically, the relationship between the fan-productions and the mothership is adversarial, and the company actually holding the licenses is never going to react kindly to that.
If Axanar's producers hadn't pushed it like they did, in the ways they did, Paramount probably wouldn't have reacted in kind. But they did and now the whole fan-film community is going to eat shit for a little bit.