They are one and the same rifle. Its just that mine has the optional barrel.
I took my "wood shroud" off because I don't like the way it looks. It has nothing to do with accuracy.
Just for information, the CG63 was made on several Model 96 actions and not just the the Swedish actions. I've had one in the past that was a Mauser stamped 96 action.
Although most of these rifles are Swedish , the CG63 really means a type of target rifle that follows a set of rules for that type of target shooting.