The 1st (Butler's) SC Infantry was the 1st SC Infantry Regulars, aka 3d SC Artillery. The 1st (McCreary's) SC Infantry, Provisional Army, was also known as the the 1st (Gregg's) SC Infantry, after it's first commander, Maxcy Gregg. The 1st (Hagood's) SC Infantry, seems to have been called that throughout the war, even after it was no longer commanded by Johnson Hagood.

Maybe this will clear up some of the confusion (or add to it?)