You are a resident of only one state at a time in the United States. If you divide your time between two or more states, you're a resident of the one you spend the most in in any given year. If you somehow manage to divide it more or less evenly, you get to pick which one is your "primary residence". Your privilege of driving in one state on a driver's license from another state is incumbent on being a current resident of the state that issued the driver's license. Every state (as far as I know) requires that you surrender any out-of-state license within a fairly short time after becoming a resident of that state, and if you continue to drive on an out-of-state license beyond that short time you're driving without a valid license and can be cited for a violation if caught.
Back when I lived in Indiana, Indiana was quite assiduous about going after snowbirds who lived in Indiana seven to nine months a year, and skipped off to Florida for the winter, for registering their cars in Florida, which has much lower vehicle excise taxes. The only way to get away with this is to own two cars, one of which (mostly) stays in Indiana and the other which (mostly) stays in Florida. Most states require a vehicle to be registered at the place where it is "ordinarily garaged," which may not be the owner's legal residence if the car is a secondary vehicle that is ordinarily kept at a secondary residence or some other location. Other rules apply for fleet vehicles that don't stay in any particular place for any period of time.
As an aside, if you split your time between two or more states, you probably have to file state tax returns in all such states.
As a second aside, if you leave the United States and take up a residence in a foreign country, you continue to be a resident (technically, a "domiciliary") of whatever state you last resided until you either establish a residence in a different US state, or you relinquish your United States citizenship. You can also be a resident of a US state that you've never lived in, if you are a US citizen by right of birth born abroad, in which case you inherit your domicile from whatever your parents' domicile was at the time you become an adult (if they differ, you get to choose). This matters because expats and citizens born abroad vote in national elections through their state of last residence (or imputed last residence, for citizens who have never resided in the United States).
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