Prepaid cards have numbers that identify them.

Which, btw, makes perfect sense. As a shop that takes credit cards, I would want to know if someone has signed up for a subscription service with a prepaid card, since the card may run out, prematurely cancelling the service.

There's a big database at the backend of the credit card processor that keeps track of all this stuff. The shop can tell a lot about you based on your card number.