8 1/4" differential

You can use a used ring gear on a different used or new carrier without any problems but the ring gear needs to be used with the original matching pinion gear (because of wear patterns).

You are right on the different carriers. The 8.25 rear uses a different carrier for the lower gears up to 2.76 and another carrier for any gears that are steeper than that.

So if you want to switch the gears from a 2.44 to a 3.23 or 3.73 you'll have to source another carrier since the one from your 2.44 will not except those higher ratio ring gears.