Sounds like South Carolina follows a Westminster style government. Look at the UK, NZ, AU governments (and I assume Canada, don't know for sure): A King, or Governor-General, with the theoretical power to override parliament. A Head of State which can issue decrees and makes important decisions "on the advice of the Prime Minster".

Basically a figure head and a bunch of legal fictions wrapped up in the concept of "The Crown". But the real power lies with the PM and their Cabinet. But the party in charge can change the PM whenever they want, and if it ever got bad enough Parliament can change the party in charge without waiting for an election.

The PM is responsible to the Cabinet and to their party and to the rest of Parliament. It is all one big mess of ambitious people pointing guns at each other, constantly evaluating their position ahead of the next election.