there's no wiki, but i would guess bare_back refers to completely exposed/unclothed back of a character (with no dangling articles of clothing) while back refers to the posterior part of the torso (not necessarily exposed) like post #5113 and post #10278.
however, it seems like both tags need massive cleaning (if even it's practical) to delineate the two. i'm not so sure now if that's the original intention of the tag usage.
Updated