Not so long ago it was common enough in some places to have to go inside, give them X cash, then pump, then come back inside to get change - they would set the pump to only dispense up to X. It's basically that system digitized.

If you go back far enough the only record was on the pump itself, so it was either full service, or trust people would come in a pay what they pumped. People did just drive off sometimes in that case, but at least in the full serve case, you still had their gas cap and plate number, which was a disincentive.

It's the same concept as paying for a meal at a sit down restaurant: they authorize your card for the check amount plus some extra, then you write in the tip on the receipt, then the restaurant captures the correct amount later (at least, that's historically how it works, many restaurants are shifting to payment terminals where it's all done at once).

When I went on long driving trips, gas station attendants would be confused when I went in to get $20 on pump three but hadn't pumped. I haven't been out on the road and paying cash for gas in a long time though, I think there's probably some stations where you can pay inside after you pump.

Yes, you just pumped however much gas you wanted and paid inside. This was before there was credit card readers on the pumps. Closer to 20 years ago.

If you pay outside (card), you control both cost and volume. But it pre auths $100 or something.