Technically speaking the ring & pinion are not a part of the diff - the diff would be the piece that the ring gear fits over & bolts onto - essentially a housing containing a pair of side gears and 2 or 4 pinions - and you can swap the pieces from one diff to another.
You can also swap a ring & pinion from one diff to another, but mixing ring & pinions is a major no-no - even if they are the same ratio - when they leave the factory they are lapped to create a matched gear set, and if you swap you're likely to end up with a noisy gear set.