Last time I visited it went like this:
1. I get a bill ($50 for example) and give the server my card
2. A card payment notification appears on my phone for the $50 payment with my bank
3. The receipt comes back with a tip field where I write $10 and sign
4. The server now updates the payment and a few days later when the payment clears, the amount has changed to $60
But what if the server chose to enter $20 instead of the $10 I specified? Do I have to keep the receipt and remember to go check that the cleared payment matches a few days later? How else would that be caught?
In the UK, you enter the tip on the card machine when you put your card in, so the payment is immediately taken and everything is clear. I really want to know why I shouldn't worry about the above scenario next time I cross the pond!