prototypes help one discover if their Product (part, component, assembly) will properly function (move, install, remove) around the operational environment (sub-assembly, system, plant, operator space) during operation (or assembly, manufacture, decommissioning, service, etc).
I like how you tried to categorize prototypes, and think it can go much further.
Practical prototypes might be thought of a physical manifestations of the product prior to production. You coined the term “presentation prototype” and “proof of concept”.
You also propose the term “visual prototype” while one could refer to a “virtual prototype” might be any version which is not corporeal in nature, but meant to convey some aspect of the physical (whether a representation of computational predictions of material mechanics during production or operation of the prototype).
You are welcome to join a larger discussion: http://virtualreality.esi-group.com/work-meets-play-virtual-reality-engineering