Are MAD and AMV synonyms for Anime Music Video? On youtube and elsewhere it's frequent to find "MAD" video, a sort of Anime Music Video (AMV) composed by anime sequences on a music track. Are MAD and AMV synonyms? If not, how these differ from each other and what MAD means?
MAD are probably refer to a broader classification of AMV from Japan.

According to the Nico Nico Pedia: 

MAD refers to video and/or audio created by editing and rearranging existing video or audio, to give it new meaning. Basically, they are derivative, fan creations.

The name is probably derived from "MAD Tapes" from the 80s-90s which was the fad in which people uses cassette tapes and mess around with the audio. The acronym for MAD predates the popular usage of the term "anime."

MAD can be used to describe the the Japanese underground media community. However, MADs can be mush-ups of anything from audio clips, edited pictures, to wholly originally created content (e.g. custom animation). While not all MADs are associated anime or manga, most of the more popular ones typically are.

AMVs on the other hand typically describe the American media subculture of editing bits of anime with music, though similar in content the scope tends to differ.

Lets compare this AMV: http://www.youtube.com/watch?v=v9dHD1JvUXo

to this MAD: http://www.youtube.com/watch?v=XRHItX-zQCo

The MAD mashes up a lot more custom together compared to the clips in the AMV.