Yes, your resident state will tax you on all income from all sources. That is the same for all states.
Most states including MD do give a tax credit for taxes paid to another non-resident state to mitigate the double taxation. You are also correct that the tax credit will not be dollar for dollar to cover the all the MD tax. Basically, MD taxes at their rate and SC taxes at their rate so the credit will be the lesser of the SC tax you paid on the income or the MD tax on the income.
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