Interior Door Mortice Latches
Door latches are a very simple form of keeping a door closed; mostly with no locking or security solution incorporated. This makes their primary use internal, "passive" doors, where locking is not required but having something there just to keep the door closed when you want it closed is needed.
There are various types of latch, including tubular latches, flat-pattern latches (or "flat latches"), DIN latches which are sized accordingly with DIN Standards, and then standard latches which are the same size as a typical sashlock case.
The most common is probably the tubular latch. These are small, extremely easy to fit, and are incredibly inexpensive. These have somewhat superseded the flat pattern latch, except for the fact that flat pattern latches still more often than not stand up as a more durable option with heavier graded internals.
Full-sized latch cases and DIN standard latches are both more or less purely for fitting on doors where the door has already been mortised in a way that is designed to accept deadlocks and sashlocks, and if you wish to fit a latch in there, then you'll need these full-bodied latches.