Yes, South Carolina is a commonwealth.
Clarification: In the US, "commonwealth" = "state" legally. Four states use the word in their official name:
The other 46 (including South Carolina) are states—but all 50 are commonwealths in the political science sense: a body politic founded on law for the common good. The term distinguishes republican government from monarchy.
Virginia's case: It's officially "Commonwealth of Virginia" but doesn't use "Commonwealth" in daily style (e.g., "Virginia Department of..." not "Commonwealth Department of..."). Kentucky, Massachusetts, Pennsylvania do.
Puerto Rico & Northern Mariana Islands are US territories designated as commonwealths—a different legal status (unincorporated).
So: South Carolina = state = commonwealth (lowercase). No legal difference.