It entirely depends on the payment methods supported by a merchant. Theoretically, any bank card should be accepted, whether it’s a debit, credit, or prepaid one. In practice, some merchants accept only credit cards, for instance. The more types of cards you allow - the more potential customers your company can have. There’s no need to exclude any type of bank card from the list of available payment systems because, in such a way, you may lose clients who use only this particular payment method.