Am I part time state if I'm a student in a different state?

It might depend on the other state, but normally a student is a resident of the same state as the Taxpayer that claims them. The dependent student files a non-resident state return for the school state to claim the income earned there. Next, they file a return for their resident state and claim all their income. 

The resident state will give credit for the tax paid to the school state. 

In this scenario, do the non-resident return first, then the resident state so TurboTax can calculate the credit from the tax paid on the non-resident return. 

If the student is not a dependent, they most likely would be considered a Part-Year or Full-Year resident of the school state.