Roughly [US]:

Creditors are usually banks (or credit unions), i.e. Chase, Citi. These organizations are taking the risk. They earn their money from interest, annual fees, and probably a piece of the transaction or from the relationship with the network.

Above, I probably should have been more clear and will fix that post.

Networks are the cards: MasterCard, Visa, Discover and AMEX These are the organizations processing the payments. They earn their money via a small piece of each transaction. As a network, they have no risk.

Note: between the two above are middleman processors. A merchant wanting to take CC's opens an account with a processor, who makes the connections. These folks get a cut of each transaction and sit between the merchant and the card networks.

AMEX is a network, but they also became a bank recently. Other banks put cards on the AMEX network. When a bank like Citi does they have the risks. When AMEX does, they do. (examples, Charge cards, AX SPG, AX Delta and so forth are AX Cards. The Citi American Airlines AMEX is a Citi card processed on the AMEX Network.)

Discover is a network and not a bank. They issue directly and don't let others like Chase do it for them, so they take all the risks and get all the profits. Update: See post below, looks like Discover is getting into branded cards.

A simple graphic can be found here