When the payment is done via a network such as VISA or Mastercard (which in some countries such as the UK which do not have their own card payment networks are the only networks for both Credit and Debit cards), the payment might be made without checking if the account linked to the card has enough to cover it (even for cardholder present payments, i.e. you're paying yourself at the machine with the physical card, not using the card numbers), and if you have not arranged with the bank to have overdrafts authorized in that account there will be an "unarranged overdraft" and some banks charge you a lot for it, in some case even do it per day the account is in overdraft.

In countries with their own card payment networks, the network only does debit payments and as part of the protocol the system first checks the account to see if it can cover that payment and only then accepts (or denies) the payment.

The issue is theft. In the US a debit card transaction dispute takes months to resolve and you may not get all your money back. So when your card number is stolen and used, you're out a lot of money for months and some you never get back. CC disputes are reversed in the card holder's favor immediately.