I am aware of some third-party online payment processor. However, I’ve seen some sites who doesn’t state which payment processor they use (eg. PayPal), the only field I see are registration details and credit card information fields. What are these type of payment processors?
Example, in Linode I wonder what they use as a credit card processor.
They are called Payment Gateways. They generally come with an api. You connect, send the CC details, payment is processed, response is sent back.
A popular gateway in New Zealand is DPS.
http://www.paymentexpress.com/
They are incredibly easy to use and have different options depending on the size of your operation.