This is not the case of debit cards in Europe. Debit cards are tied to bank accounts. Most people only have a debit card or don’t even know what a credit card is (or what the difference is). We just call them “cards”.
You can buy debit (or more accurately prepaid) cards in supermarkets in Europe too (which is a big and relatively diverse place, so just because that is/was not a thing in the countries you're familiar with doesn't mean it didn't exist).