If you have to show ID to law enforcement or be fined then you are required to carry ID. Here you have to identify yourself, but you are not obligated to carry ID on you at all times. So if someone walks to a store and pays cash they don't need to have an ID and cannot be fined or punished for not having one.

It is required for something like driving as it involves a license and carrying it with you when driving is a requirement.

As far as voting goes, in rural areas, especially where everyone knows each other, nobody needs ID because everyone knows Billy was born in the local hospital and lives with his uncle and he was added to the voter role decades ago so when he goes to vote he signed his checken scratch signature and Glenda gave him his ballot to vote. Prior to ID requirements you just verbally said who you were and signed so you couldn't vote twice and this wasn't an issue ever.

The whole registration thing is so they knew who is voting where to give them the right ballot for local officials and to keep someone from voting twice and study after study showed it was not a significant problem. Requiring ID to vote only has downsides and is intended to be voter suppression in the US through cost an other obstacles.