The current laws differ between states. In some states, and the way it has traditionally been since the Voting Rights Act, your identity is checked through:
a)registering to vote in the first place
and
b)stating your name, address, and sometimes party registration to the voting official
This is more than sufficient, as your polling place has a list of all people registered to vote at it. If you try to vote anywhere else you can only get a provisional ballot, which must then be cured after the fact. The polling place then crosses off your name as having voted.
If someone were to try and vote in your name, you'd figure it out when you arrived and your name was already crossed off. Similarly, if you arrive first then the fraudster would be in serious trouble. And for this reason there is negligible fraud already.
What the GOP wants to do is pass laws requiring extra gates of identity checking, weighted to not hinder wealthy landowners and to most hinder anyone who would vote against them. For example, in some of these "Papers, please" laws you're allowed to vote if you show them your home's utility bill, which in no serious way identifies you as you, while at the same time photo ID cards issued by tribal governments are "non-qualified ID".
"Oh, but just don't do it like that", you say? No. It will be exactly like that if you fall for the GOP psyop. That's the whole purpose of passing the law, because there is no significant fraud without it. "Papers, please" laws are naked voter suppression, one more weight on the side of shifting elections towards Republican victory.