I'm not sure there is a massive difference to be honest - that's the problem with stealing someone else's spreadsheet then finding it doesn't make complete sense when examined closely!
I guess wallpapers are specifically created so as to be wallpapers regarding the dimensions, and sometimes it might mean certain design elements so that desktop icons aren't lost in a too-busy graphic? Something like that! I don't myself think it matters - call them wallpapers if that's what you created them to be (and if people want to admire them purely as 2D art that's great) or call them 2D art and if people can use them as a wallpapers, all to the good.
Your other question was, I think, what if the primary work is art (like wallpapers) and someone does a complement for that art which is also wallpapers? Well, it could happen, but honestly, I've never seen it. People tend to offer complements which are...complementary, by which I mean they add something a little different, they go off at a bit of a tangent in some way. The commonest way to manage that is to do a complement in a different medium. But people do do complements in the same medium as long as they're pretty different from the primary work. Like if you made wallpapers, someone might do a linked icon set as a complement.