Types of Hinges:
Full Mortise - Both leaves are mortised. One leaf on the frame and one leaf on the door.
Half Mortise - One leaf is mortised to the door and the other is surface applied to the frame.
Full Surface - Both leaves are applied to the surface. One to the door and the other to the frame which may be a metal core door or hollow metal door with channel iron frame.
Half Surface - One leaf is mortised to the frame and the other is surface applied to the face of the door which may be a wood door with a wood frame or a metal core door with a hollow metal frame.