Not necessarily. (Although if this is a permanent move, you will want to change your driver's license and state tags to your new state as soon as possible)
If you moved to SC for a temporary work assignment, then you would file a GA resident return and a SC nonresident return. You would get a state tax credit for SC taxes paid on your nonresident tax return on your GA state tax return because you would have to report all income (including SC source income) on your GA resident state income tax return.
However, if you moved from GA to SC with the intention of making SC your new state of residence, then you would file part year returns for both GA and SC and report income for sources both inside and outside the state for the portion of the year you were a part year resident in each state. If you rent a home or apartment in SC, that could be considered as part of your intention to permanently move to SC.
Check
below for more information about filing a part-year state tax return (Please
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https://ttlc.intuit.com/replies/3302008