The way the European system works is that there is one possible operation; the owner of an account can move money from their account to any other account.
If you want me to pay you rent, you provide me with a standard format bill, which includes your account number, the amount, the date to pay by, and an optional reference number (for use of the recipient to tell what I was paying for). To pay, I input those into my banking app (or more likely, read the barcode on the bill with my phone), verify that everything is correct, and press a button to transfer funds.
The point is, I don't have to trust you to do any of the banking right. I have paper trail from you in form of the bill you provided (which confirms that the numbers I used are correct), and from my bank that the transfer was initiated on a given day at a given time. There cannot be any error that I didn't make.