This article is from the Credit cards and Consumer Credit FAQ, by email@example.com (Steve Adams) with numerous contributions by others.
As its name implies, it is not a credit card. Instead of running up
a bill for you at the end of the month, the debit card runs down
your account at the moment the sale is made. Merchants like these
because they get instant payment without worrying about bad checks.
Debit cards are convenient. But it's a lot more painful to resolve
a problem if the money is gone from your account (as with a debit
card) than if it's just numbers on a piece of paper (as with a
credit card). And if you lose a debit card, your whole account can
be cleaned out with no recourse for you. You decide whether you
want to take on that risk.
A reader has reported that his Schwab account has a debit-type card
associated with it, but it is treated like a credit card for other
purposes. In other words, it is a credit card, but the debit is made
immediately to his Schwab account.
Consumers in the know don't like debit cards because they give you
less protection in case of disputes than credit cards do. (See
section 5, "Billing errors and overcharges.")