There is also a system for manually configuring a link to a payment processor that includes hosted secure pages as part of their service; we call it the the custom gateway method.
Nearly all payment gateways can be setup to collect credit card data by posting to them a form created of hidden fields. In this case the secure pages are hosted on their server and they simply require details about the order. The payment gateway may or may not return information to the cart as to whether the the customer's card was accepted.