Tabletop:
You takeoff, clear a flat area, and then there is a sloped landing on the other side. You don't land much higher or lower than the takeoff.
Step-up:
The landing is noticeably higher than the lip of the jump.
Step-down:
The landing is noticeably lower than the lip of the jump.
Hip:
Very steep takeoff, and you land on a slope that is perpendicular to the jump. Basically, a lot more up and to the side than out forward.
Quarterpipe:
A wall of a halfpipe, without the full pipe.