Identified by a single handle that moves over a rounded ball shaped cap right above the base of the faucet spout.  Delta and Peerless are common ball-type faucets.

Cartridge faucets operate with
a movable cartridge that moves
up and down to regulate flow. Identified by an up/down
motion of the handle rather
than back/front as with a ball
type faucet.

Identified by their single lever over
a wide cylindrical body. These faucets have a cartridge that holds ceramic discs which slide over
each other to control water flow
and mixing temperature.

Most easily identified by their separate hot and cold water handles. A compression stem requires you to tighten the
handle in order to stop
water flow.