Both MasterCard and Visa offer both types of cards. I've got two different Mastercards from my bank. One that is a debit card, draws money directly from my account and stops working if there is no money in the account. The other is a credit card with a line of credit, a bill at the end of each month and an option to only pay off a small part of what I owe.

That being said the debit card version is the one you get by default, and the credit card version is something you have to ask for separately.