A bootleg is where you take a track, and change it radically - new BPM, genre, new instruments, vocals and so on. Think of it as a "DIY remix". A mashup is two or more existing tracks, creatively combined to make something new. A re-edit is where you alter an existing track by lengthening it, shortening it, rearranging its parts and so on (this is often done to make it easier to DJ with).
In today's world, where all DJs have access to pretty much everything, making re-edits, bootlegs and mashups is the best way to make tracks nobody else has got, to DJ with. Also, you can produce remixes that you could never perform "live" in a DJ set otherwise, even with the best features of the most modern DJ software and hardware.