Do these 60s kitchen drawers have narrower boxes than the faces?
This style of cabinet is called a "face frame". Its typically an American style cabinet that is a little easier to install but you lose access to some space since the opening for the door is smaller than the carcase of the cabinet. Typically there isn't a smaller box inside its just a frame around the door.  Contrast this with European style cabinets where the doors and drawers cover the full front of the cabinet box.