No, they will charge you a fee called an overdraft fee for the "service" of allowing you to purchase the item. They basically extend you a small line of credit

No, they will charge you a fee called an overdraft fee for the "service" of allowing you to purchase the item. They basically extend you a small line of credit (there's some upper limit before they will deny the purchase) and then charge you, say, $35. Credit cards are always overdrawn in the sense that the bank has extended you a line of credit, but they don't have a fee associated with typical use.