Voting in person in the US usually involves a checkin process where an election worker looks up your name and address to 1. Confirm you are registered to vote, 2. Confirm you are in the correct location to vote, and 3. Confirm that you haven’t already voted.
After voting you follow a similar process to check out, so they have a record that you checked in, voted, and checked out.
Point 2 is because in larger towns & cities there are often multiple voting locations, and voting locations are based on where in the town you live. For example in my city I vote at a church two blocks away from my home. If I tried to vote at a different location in my city they wouldn’t allow it, and would tell me to go to that church. (I think I could cast a provisional ballot at an alternate location if I provided sufficient ID, but that vote would only be counted after the election ended and records showed I didn’t vote at my usual location.)
Voting in person in the US usually involves a checkin process where an election worker looks up your name and address to 1. Confirm you are registered to vote, 2. Confirm you are in the correct location to vote, and 3. Confirm that you haven’t already voted.
After voting you follow a similar process to check out, so they have a record that you checked in, voted, and checked out.
Point 2 is because in larger towns & cities there are often multiple voting locations, and voting locations are based on where in the town you live. For example in my city I vote at a church two blocks away from my home. If I tried to vote at a different location in my city they wouldn’t allow it, and would tell me to go to that church. (I think I could cast a provisional ballot at an alternate location if I provided sufficient ID, but that vote would only be counted after the election ended and records showed I didn’t vote at my usual location.)