Kein's right - e.g. a caster head will give you hands, but a warrior's head will have your arms ending in blades.
I'm pretty sure I also noticed that some chest pieces look different regardless of the head. But this only seems to relate to type, not quality, so a 'Well Preserved' piece will look identical to a 'Perfect' piece.
I can confirm that any body parts you 'bank' with a necromancer will be available for all other necromancers. E.g. the necromancer in the FoV expansion had access to my full set of parts from the first time I met him. Unfortunately, once 'banked' you can never get that part back (e.g. to sell once you find a better part). But any further copies of that part you might find will stay in your inventory and you can sell those.