The difference is that with a credit card, they're taking the bank's money, and you're not paying anything unless and until a bill comes. With a debit card, they're taking your money out of your checking account. Yes, you can dispute it, but potentially thousands of dollars of your money are tied up in the process.

Case in point, I know someone who was in a rental car that got totaled. The rental company charged his credit card for over $20,000 a week later. The card company held the charge until the secondary insurance coverage process was completed. He never saw any money leave his bank account. Had he paid with a debit card, he would have.