A quodlibet is a piece of music that features a combination of melodies, for example, popular tunes. They are typically combined in a surprising way that makes them funny (especially if you know the typically non-funny intent of the original tunes).
A mashup combines two or more pieces of music, sometimes superimposing the vocal track of one song over the instrumental track of another.
Either may consist entirely of other people’s music. The art is in the blending.
Grant Woolard has combined 57 classical themes by 33 composers in this clever YouTube video. The graphics are as entertaining as the music.