Credit card can work offline, they just record your credit card number, the amount, and your signature to approve the transaction. In old days, they did that by pressing carbon-copy paper over your credit card.
Later, they will take this transaction info to the bank, and I think credit company might pay the seller even if your credit card is over balance (they will charge you the overdraft fees). So no risk for the seller.
With debit cards, they need confirmation from the bank that there is enough money in your account. I am pretty sure that without explicit overdraft protection service, a bank will reject debit transaction.
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