As far as I know, Mirror Universe is actually the specific case, the Star Trek "Mirror, Mirror" Spock has a beard universe. Although not actually necessarily specific to Trek fandom, just specifically "everyone is evil and/or openly bisexual" as seems to um, be the trend in the Mirrorverse.

Parallel Universe -- it seems like that really only applies some of the time? Some of them are wish 'verses or dream 'verses or alternate/collapsed/paradoxical timelines or whatever. What their common thread is, is that canon produced them and gave us a glimpse. I don't know how you signify that without somehow saying they're from canon.