He's not asking about the club card, which is something separate. It's a card that the store issues to regular customers that allows them to get special sale prices or deals. When you check out at the grocery store you give the cashier your club card first, and then pay. "Will this be debit or credit?" means "will you be using a debit or a credit card to pay?" In most US stores your don't give the bank card to the cashier but swipe it yourself in a small machine. If you use it as a debit card, the money is immediately withdrawn from your bank account, or from the balance of the card, depending on what type of debit card it is. With a credit card you are billed later for the amount.

A debit card pays with your money from your bank. A credit card uses the banks money, that you have to repay, usually a little each month. A club card gives you points that mean you are a frequent customer, and can get extra discounts. "Will this bec" is incorrect English. Maybe this text was copied incorrectly?

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.