A debit card is a card linked to the money you have in the bank. A credit card gives you a loan when you make a purchase that you pay back later. Club cards are either small store based credit cards or cards that give a reward for shopping like cash back. They ask because there's a fee to the store to process credit cards and they keep track of it so they can pay for it. If you're unsure what you have you can always say credit but can only say debit if you have a debit card.