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The very elaborate, meticulously-edited AMVs set to popular music that you see from creators like Nostromo are, as far as I know, mostly the domain of non-Japanese fans. Naturally, I can't prove that there aren't any made by Japanese people, but I've spent my fair share of time bumbling around on Niconico, and haven't seen anything of the sort.
What ...
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This seems like an awfully fuzzy thing to try to delineate. I'm going to claim that the answer to your question is "you classify an AMV as an ASMV whenever you think that sounds like the right thing to do".
See, the thing is, "ASMV" is strictly a piece of fandom jargon that sees no use outside a small sub-subcommunity of the subcommunity of AMV creators. As ...
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I found the video: http://www.nicovideo.jp/watch/sm2931268
The tags I was looking for are: ツッコミカルタ and アニメかるたリンク
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I think MAD and AMV is one. MAD is shorted for "music anime douga", similar to "anime music video" aka AMV. There's lots of pages saying that these two are actually one kind of fan-made video, too.
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