It depends. You will usually be taxed on all of your income by your resident state. If you work in a different state, that state may tax you on the earnings there.
When you live in one state and work in another, you often need to prepare two state tax returns - a nonresident return for the state in which you work and a resident return for the state in which you live. In this situation, you generally prepare the nonresident state return first. Follow the prompts in the nonresident state return in TurboTax to identify which income from your Federal return is sourced in that state. If there is tax due to that state, you may be able to claim a credit on your resident state return for the tax paid to the other state.
Some states have reciprocity agreements so that you don't have to prepare two returns if you only receive wages in the nonresident state.
See this article for information on states with reciprocity agreements.
See also this TurboTax article and this one on multiple-state situations.
Shouldn't all the state wages on the W2 add up to the federal wages?
Some states, New York for example, require that their Box 16 amount match the Box 1 amount regardless of whether or not all your income was earned in New York. In these situations you may have to adjust the W-2 amounts when you do your tax return.
So all state wages should total the federal wage amount?
@lfrugoli953 --
Not necessarily, for the reason given in my previous post. For example, the Box 16 amounts for a taxpayer who works in NY and another state might total to more than the Box 1 amount.