Don't believe everything you get on this site, 90% iof the people answering questions have no idea what they are talking about. The laws vary from state to state. In PA a sheriff does not even have the power of arrest at all! Your question about jurisdiction is valid, you should be able to find out the powers of S.C. sheriffs online.
A sheriff can pull you over for speeding even if they are not in their country. Even though their duties vary from country to country, they are administrative legal officers who are hold the executive power. If they pull you off, they will then hand you over to one of his like in your country.
I love the answers! It varies by state, Colorado you have full police powers from county to county, unless it is Indian reservation land, then your just a visitor. Michigan used to be county by county. The statement most often seen is "Cops can do what ever they want!" That is false, we can't do as we wish. Never could, never would. Check with your own states laws on this if you want a quality answer!