It's a debit card with some credit card features - that's all. It's tied directly to your checking account because you aren't buying things on CREDIT, you're buying things with the equivalent of an electronic check...a.k.a. a debit card.

If the card came with your checking account, it's a debit card, not a credit card...case closed.

ETA: And, to further prove my point - have you ever paid an interest charge on this "credit card?" I'd say "no."