Why are my debit cards treated as credit cards in several Latin American countries?

I have several Visa and Mastercard debit cards, each associated with a checking account of a British bank. Although my cards are debit cards, I have checked in several countries that they are treated as credit cards. The countries I have checked so far are Peru, Bolivia, Chile and Argentina. Why is that?

Edit: Many POSs in these countries only accepted debit cards, which meant they did not accept my cards because of the above. Even if credit cards were accepted, the employee had to explicitly state that my card was a credit. When the direct debit was withdrawn, the POS issued an error with the wrong menu. I wonder why that is.