If the booking is prepaid or if the room is simply guaranteed with a credit card, it doesn't matter. The hotel will ask for a credit card at check-in, to cover additional expenses you may incur. They may or may not be okay with a debit card or cash deposit in lieu of a credit card. For example in China they sometimes will take a couple night's payment as a deposit in cash and you get back any unused funds when you check out (provided you didn't lose the flimsy receipt).
The credit card you present need not be the same as the one used to make the booking, and typically when you check out you have another opportunity to either leave any charges on the credit card you gave them or put the charges on a different credit card (or pay cash).