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.