Since the motor voter bills in the 90s. Most US states handle voter registration via the Department of Motor Vehicles (DMV). When you apply for your license or renew you tick the box and it automatically registers you.

The drivers license database is the defaco registry of where you live and most states require you to update your address within 2 weeks of moving (although enforcement is loose). There is a state identification card for those who don't drive that fulfills the same purpose as a drivers license.

Since RealID states now have to check immigration status if you request a RealID license (some states will issue non-RealID drivers licenses to the undocumented). There is a further Enhanced ID check that some states do that will indicate that you are a US citizen on the license. RealID and non RealID licenses are clearly marked.

Basically true voter fraud is largely a non issue because the States generally have their systems together. Voter suppression, which is the goal of most of the voting related legislation of the last 20 years, is however rampant.