What sort of weird gas station requires you to specify the amount of gas before actually refueling your car? Is that a USA-only thing? Never seen that in Europe.
I don't think OP was saying that. The pump asks Y/N if you want a receipt before you pump, but prints it after the pumping.
That said, you do specify the amount of gas if you're paying cash here in the US. You go inside, say "here's $20", and the pump will dispense exactly that.
If you're paying with cash you usually have to prepay. If you're paying with card the station does a preauth on your card (and usually a temporary hold) then does the final authorization after you finish pumping and it knows the total. Sometimes you have to pump twice if you want to go over the preauth hold amount, which is usually $50.
It's worth noting that it wasn't that way the entire time I was growing up. You would pump first then pay the cashier. It wasn't until around 2005ish that I noticed signs instructing cash customers to prepay.
It's not required, but, in most self-serve stations I'm familiar with (Costco being the exception), you can prepay with cash (e.g. ask the attendant for $20 on pump 5, or whatever), and the pump can be set to stop after $20 worth is dispensed. If less than $20 in gas fills your tank, you can get change from the attendant. This is commonly done late at night or for pumps not visible from the attendant's vantage point, to prevent drive-offs.
I've seen it in Norway, Italy, and somewhere else before. It's not terribly common—or it's usually optional and most people don't realise you can do it.
Also in Italy, if you pay cash at the pump you have to specify the exact amount. And woe to you if you over estimated how much you'll need < there's no change.
This is common in Iceland as most pumps let you pay with card at the pump so you pre-auth from a number of options and get charged the actual amount you pump.
