Sorry, I believe that answer is wrong. @TomD8 is a good expert on multi-state issues.
In general, you must file a state tax return in the state where your permanent residence is located, that reports and pays tax on all your world-wide income, regardless of where it was earned or paid.
If you physically work or live in another state, you owe state income tax where you work, but only for income that is considered "sourced" to that state. If you physically live or work in OH, you file a non-resident return to the state of Ohio that only reports income earned while physically working in the state. That means, for example, that your wages are reported on an Ohio non-resident return AND a SC resident return, but bank interest, dividends, investment income, etc. is only reported on your SC return.
SC will also give you a credit to offset taxes you paid to OH for the same income, which reduces the effect of double-taxation.
Maybe SC has a different definition of in-state income, but I doubt it.
