difference in rear hub widths?
A list of hub spacings is here. Obviously, you need to have a wheel which fits into the frame and matches the hub spacing (in some cases, you can squeeze a slightly bigger or smaller hub into a frame, such as for 27" -> 700c conversions, but this is peripheral).

Normally, when you swap a rear wheel to a different one, you will need to make slight RD adjustments - there are variations to where the derailleur sees the cassette.