No.
Both those states have a state income tax.
You always owe income tax to your home state (the state where your permanent residence is located) on all your worldwide income. Then, you also owe income tax to a state where you live or work while earning the income. In this case, you will file a NC resident tax return to report all your world-wide income, and you will file a SC non-resident tax return to report only income earned while living or working in SC. Prepare the SC return first. Then on your NC return, you will get a credit for taxes you pay to SC, so you aren't double-taxed on the same money.
Because SC income tax rates are higher than NC income tax rates, you should have SC tax withheld from your job.
