There is something similar in India called netbanking. Typically, the site redirects you to a payment gateway, which then redirects you to the bank's site. You

There is something similar in India called netbanking. Typically, the site redirects you to a payment gateway, which then redirects you to the bank's site. You enter your username/password only on the bank's site and complete the transaction. It is used quite frequently due to convenience and security. When I moved to Oz and tried to buy something online, I was quite taken aback that I was being asked to enter bank login details on 3rd party sites directly. Felt completely unsafe, so haven't used it yet.