"Transaction" means to buy or sell something. The word is formal and businesslike, and includes all of the steps needed in the deal. For example, "I bought a car; I gave them teller's check for the balance, but the transaction is not complete until they send the certificate of origin to the Registry of Motor Vehicles..."
To "fulfill" something means to do everything needed to carry out a promise. When you buy things from the amazon.com website, sometimes Amazon itself has the merchandise in its own warehouse, and Amazon takes care of shipping it to you. In that case the transaction is "fulfilled by Amazon."
Sometimes Amazon lists items from other sellers... a cell phone case, perhaps. Amazon has the picture and description on its website. But it will say "sold by GreatPhoneAccessories." Amazon has the "buy" button. Amazon handles the payment and takes the money. But Amazon does not "fulfill" the order. Amazon does not have the case in its own warehouses. Amazon does not ship it to you. GreatPhoneAccessories does that. If you don't get it, Amazon will want you to talk to GreatPhoneAccessories first. However if they don't solve the problem, then you can call Amazon customer support second.
(In my experiences, Amazon has always been very good about taking care of problems, by the way, even when it was a "third party" seller).