For the year that you move you will have to file part-year resident tax returns in both states. You pay California tax on the income that you received while you lived in California, and South Carolina tax on the income that you received while you lived in South Carolina.
If you have income from a California source after you move, you have to report that income to both states. For example, if you sell your home in California after you have moved, the income from the sale is taxable by both states. But you will get a credit on your South Carolina tax return for part of the tax that you pay to California on that income, to avoid double taxation.