Not all cards are created equal.
Credit cards offer a line of credit that is accessible through the use of your card. Every month you receive a statement and you are required to pay a minimum payment.
A Charge card is similar to a credit card with the difference being that you must pay the balance off in full each and every month.
A Debit card allows you to use a card for the convenience but it basically works like a check in that it takes the money from your account and if you do not have enough money in your account the charge will either be denied or you will be charged an overdraft fee, just like if you bounced a check. The advantage for a debit card is that you are not borrowing any money but just using your own funds with the convenience of a card. Most debit cards use a PIN number but you can also have the merchant run it as a credit card and that may actually be a safer way for you to use a debit card.
Check out this FTC website that explains the fraud liability for the different types of cards.