Fluent speakers of English, I need your help?
No, it is not the same. In legal documents, it is best not to try to simplify or abbreviate the wording, which is usually very carefully thought out.
It is rather difficult to simplify just one phrase in this complicated text, without simplifying most of it. I shall attempt to simplify or summarize as much of the text as I can, and then I shall come back to the phrase that is puzzling you. The whole text means this: "General Terms and Conditions of the Bank" means the rules under which the bank works. Anyone who uses the bank's services must observe the rules, so that both bank and client know exactly what they should do, and both sides know that they are acting fairly with each other. These rules govern what the client should do when he begins to deal with the bank, in whatever way, whether it be signing up for a bank's service, or altering or, eventually, ending that service. "Entry into banking services" is a general expression and it means the beginning of some kind of business between the bank and the client. "Entry into agreements for banking services" means exactly the same as "Entry into banking services", except that it ("Entry into agreements...") relates to a rather more-specific aspect of beginning to do deals with the bank. I disagree with your contention that one cannot amend a service. For example, the bank might give you a loan to buy a building, machinery, and so on because you tell the bank that you wish to start a soap-making business. You begin the moves that are necessary to start a soap-making business, but partway through your movements towards that business, you find out that there is no money to made in it. You decide to make putty, instead, so you ask the bank to amend the agreement from soap-making to making putty. You have the money to buy a building, and perhaps the machinery that makes soap could be used to make putty. That is an amendment to an agreement. The bank has provided you with a loan, which can be seen as a service, and you wish to amend it.