If your legal residence is in SC I imagine you will need to register the car in SC and be subject to all SC taxes and fees.
I'm not familiar with NC rules, but in general states make sure they get what's coming to them - and cars are easy to track. For example, if you buy a car in a state with a 4% sales tax but live in and register it in a state with a 6% sales tax, you will be assessed and pay the 6% tax one way or the other. Perhaps 4% to one and 2% to your home or 0% and 6%... one way or the other they will make sure you pay the full 6% to somebody.