Is an independent the same as unaffilated in US politics?

They are not the same, but they overlap. To be unaffiliated means one is not connected to any formal political party. Independent voters are also unaffiliated, however, in most states voters can register officially as Independent. Thus, Independent can be an official, state-recognized political stance, whereas unaffiliated is an informal term that simply means not connected to a party. So all Independents are unaffiliated, but not all unffiliated voters are officially Independents.