There are two major aspects of a credit or debit card. There must be a payment network, where the electronic transactions occur when you swipe a card. There must also be a bank supplying the funds being transferred. The network company normally only deals with network-related services like theft/fraud and merchant relations. They need an card-issuing bank to either supply the card with a credit line (credit card), or a deposit bank account (debit card). The issuing bank is who deals with payment and collections.

Then there are basically three main categories of credit/debit cards:

1. Visa and Mastercard: These two companies are only payment networks, which is why a bank normally issues these cards.

2. American Express and Discover: These two companies have their own payment network, AND they are their own bank. That is why you will normally not see a Chase AMEX card or a Capitol One Discover card, although in the last few years, AMEX has begun licensing its network on some bank cards.

3. Store cards: A retail store can issue a card to customers. These can either be on the Visa/Mastercard network, or a private network used only at the store. The bank can either be the store itself, or an underwritten bank supporting the store.