A half mortise lock is shown mounted in a cabinet door above. With a half mortise lock, the end and one side of the lock is exposed on the back when installed. A full mortise lock only has one end exposed.
Half mortise locks became popular by craftsmen because making a wide shallow cut and fitting the lock flush on the instide wasn't too dificult. As you can imagine, installing a full mortise lock requires more precision. Usually half mortise locks do not have a strike plate. Instead the lock engages into a slot simply cut on the opposite side of the piece.