Is it safe to assume all references to AD&D (and the adnd tag) are references to the 1st edition (1e) version of the game?
I can't speak for how everyone will use the term in their questions... :)
adnd doesn't need a "1" qualifier. 1) Almost all AD&D 1e questions are relevant to AD&D 2nd edition since it's not significantly different in most regards. 2) If people say "AD&D" without qualifying, they mean 1st edition. 3) If people mean 2nd edition specifically, they invariably say 2nd edition. Hence adnd is a better tag than [adnd1] would be, is more natural, and doesn't cover anything it shouldn't.
Looks like we need to add some definition to the wiki exerpt...
AD&D 1e and AD&D 2e are substantially different. Notably, 1e was written during the golden age of the 1970s, solely by E. Gary Gygax; 2e was written in the late 1980s, by David "Zeb" Cook after Gary was ousted from TSR. The differences are myriad (the biggest being Skills). Note that at Dragonsfoot.org, two thriving and separate forums address 1e and 2e.
I strongly suggest that AD&D1e and AD&D2e be separate tags, and the generic AD&D tag be retired/redirected.
AD&D 1e and AD&D 2e are similar in a lot of ways. Obviously they're different too, but if you compare the BD&D line (B, B/X, BECMI, RC, WotI, CD&D) then the similarities are more apparent. I'd suggest that AD&D applies to both, and asking for a specific edition be clarified in the question. It's quite possible that the answer is the same in both editions, and if someone asks a question about 1e, all that's necessary is to qualify that the experience comes from 2e.
This would be similar to asking a question about d20 and not specifying 3e or 3.5.