I understand that credit cards extend credit to customers. And that purchases incurred before the credit balance is due are nothing more than IOUs to the bank issuing the card (and also the card provider?).
But what is actually happening every time I pay off my credit card? Am I 'settling' with the bank and/or card provider by wiring them a final payment that is actually settled?
When you have a credit card account, your agreement is with the bank that issued your credit card. The bank is the one that is directly loaning you money. The credit card network (MasterCard, Visa, etc.) is essentially the middle-man. They are not directly loaning you money or paying the merchants; they just facilitate the transactions between your bank and the merchant’s bank.
When you make a purchase with a credit card, the bank pays money to the merchant and then adds that to the balance you owe on your account. Assuming that there are no disputes with the merchant about the transaction, the bill is already settled with the merchant. Whether you pay your credit card bill or not, the merchant gets paid.
When you pay your bill, the balance of your credit card account goes down by the amount you pay. You are settling your debt with your bank. If you do not pay, it is the bank to whom you owe money, not the merchant or MasterCard/Visa.
Yes is the answer to your actual question.
Actually, in both the U.S. and Europe you have a bank that is the 'issuer' of the card. Why a bank? Because banks lend money, and with a credit card they are loaning you money until you pay. Even with both American Express and Discover, your card is issued from a special bank likely named something like "Discover Bank, N.A." or "American Centurion Bank, N.A.". And, to make it more complicated yet, while Amex is its own company, Discover is owned by Morgan Stanley, the large brokerage firm.
The logo is usually more prominently Visa or Mastercard (or Amex of Discover). This is the network over which many banks record and pay merchants. It may or may not be owned by the issuing bank.
If you read the tiny type on the information on your account this will all be laid out. The letters "N.A." (meaning North America) in the name of an entity is usually a U.S. bank. Ultimately, you borrow from them and they pay the merchant through one of the networks (Visa, Mastercard, Amex, Discovery, etc.). Then, they collect from you for the money they fronted to the merchants.
The working of credit cards is often described in terms of what's called the "four party model". These parties are the merchant, the acquiring bank, the issuer, and the cardholder. There's a fifth party of the network, but they are in some sense not as directly involved. The issuing bank is the bank that issued the credit card, and the acquiring bank is the bank at which the merchant has a bank account for the payments to be deposited into.
When you put your card in a POS (point of sale/service) terminal, the merchant sends a message through their acquiring bank through the network to the issuing bank. If the issuing bank authorizes the transaction, that means that they are guaranteeing payment to the merchant/acquiring bank. From that point on (barring complications such as valid chargebacks), if you don't pay, it's the issuing bank that takes the loss. For taking on that risk as well as facilitating the transaction in general, the issuing bank is paid what's called an interchange fee by the merchant.
There is then a settlement where the issuing bank transfers money to the acquiring bank. Once that happens, the merchant has received their money and doesn't have any claims against you. The debt is fully to the issuing bank. When you pay your credit card bill, you're reimbursing the issuing bank for the money they've already paid out.
