We've been accepting credit cards for about 10 years, but I've recently been looking into all of this because (1) I'm pretty sure we are getting reamed on fees by some of our current providers, and (2) we are starting a new line of business under a different brand name and want to set up credit card processing for it.
The following brain dump of what I've found out might contain some things of use to you.
First of all, don't feel bad if you find payment processing confusing. I've found no site or combination of sites that is able to explain what actually goes on and who all is involved in credit card processing. Braintree has some good attempts at explanations, but they are not complete. Other resources I've found explain some of the other parts.
Two things complicate this. First, many companies provide many different services. If a company is providing both payment gateway services and merchant account services, they tend to merge those in any documents they write, because they want you to end up using them for both. Second, there is inconsistent terminology. Different companies sometimes use different names for the same thing.
Anyway, putting together all that I've been able to figure out so far, these are the entities that have their hand somewhere in your credit card processing. I would love corrections to this. I think I'll try to put together at some point some nice diagrams in OmniGraffle and put this up on the web (after any corrections are applied). When I first use a term I'll put it in quotes, and than put it in all caps in subsequent items.
I'll write this as if you are using separate companies for everything that can be separate.
1. Your "customer".
2. The "issuing bank". This is the bank that issued the credit card to the customer.
3. You, the "merchant". I assume no explanation is necessary for this item. :-)
4. Your "regular bank". This is the place you have your normal business account, and doesn't have anything particular to do with credit cards. It's just a place you keep your money.
5. The "credit card associations" are organizations like VISA and MasterCard. VISA and MasterCard are owned by the ISSUING BANKS. I'll get into their role in a bit.
6. Your "acquiring bank". You have a "merchant account" with them. When a transaction settles, this is where the money from the ISSUING BANK ends up. The ACQUIRING BANK then transfers the money to your REGULAR BANK, after deducting their fees. The ACQUIRING BANK is a little confusing because it is not really a bank. Their main role in this dance is to provide you with a line of credit in essence. If you sell a bunch of goods, the transactions settle, and you grab the money out of your REGULAR BANK and disappear without bothering to ship product, it is the ACQUIRING BANK that ends up coughing up the money when your CUSTOMERS call their ISSUING BANKS and demand that their charges be reversed. (Accordingly, this means that your ACQUIRING BANK is going to give you the biggest financial colonoscopy in this process).
7. A "member bank" is a financial institution that had a relationship with a CARD ASSOCIATION that allows them to function as an ACQUIRING BANK for cards from that association.
8. An "ISO/MSP". Those stand for "Independent Service Organization" and "Member Service Provider". These are essentially affiliates of MEMBER BANKS. They can sell you a MERCHANT ACCOUNT from the MEMBER BANKs they are associated with. I believe that ISOs and MSPs are basically the same. ISO is the term VISA uses, and MSP is the term MasterCard uses. You might think it would be best to get your MERCHANT ACCOUNT directly from a MEMBER BANK, but from what I've read it is often actually cheaper from an ISO/MSP. Also, just because an entity is a bank doesn't mean it is a MEMBER BANK. For instance, if you go down to a REGULAR BANK like BofA or Wells Fargo, they will happily sell you a MERCHANT ACCOUNT, but they will be doing so as an ISO/MSP for some MEMBER BANK.
9. A "front end processor". This is an entity that is hooked up the the CARD ASSOCIATION networks and can actually conduct credit card transactions. Your ACQUIRING BANK has a relationship with the FRONT END PROCESSOR.
10. A "back end processor". This is an entity that can actually initiate the transfer of money (via the Federal Reserve system) from the ISSUING BANK to your ACQUIRING BANK. Collectively, I've seen many people call the combination of FRONT END PROCESS and BACK END PROCESSOR a "payment processor".
11. A "payment gateway". This is what your shopping cart actually talks to, or (if you are actually physically accepting cards and swiping them) what your terminal is connected to. Its job is to accept requests from your cart ("Charge $49.95 to 5105105105105100") and then communicate with the FRONT END PROCESSOR that has a relationship with your ACQUIRING BANK in order to get the transaction conducted.