1. Partial Inset. Doors have a rabbet, or notch, cut into the outside edge so that only a thin lip overlies the face frame. Often fitted with knife hinges (shown), but can also use cup or surface hinges. Unnotched doors that cover a portion of the face frame are called partial overlay.
2. Full Overlay. Doors completely cover the front of the cabinet, no face frame required. Uses cup hinges, which are hidden when a door is shut.
3. Inset. Doors fit perfectly flush with the face frame. Typically used with butt hinges (shown), but also works with cup, knife, and surface hinges.