I will have to agree, you have a credit card, if you go to a ATM and use it, you get cash that is charged against your credit card account.

If you go to a ATM and use your checking account card ( the money is taken from the bank account)

So do you really have a credit card or is it just a ATM card that is linked to your checking account, ( normally called bank card) those are issued for your checking account and are not a real credit card.