Answer:
Yes. You can use your debit card as a credit card. When you run it as a credit you will almost always have to sign for your purchase, but when you run it as a debit you use your PIN number. With the debit the amount is deducted immediately from your bank balance, ran as a credit it doesn't show up until the next business day or two later. It doesn't have anything to do with 'your credit'. Just another way merchants can run your card.
Usually how to run it as credit is on the pad where you swiped your card instead of entering your pin you hit cancel and that will run your card as credit. It still isn't necessarily a credit card as you cant accrue debt on a debit card.