There are three types of payment gateways:

1. Hosted: The payment gateway takes customers off your site to the payment gateway page. Once payment has been made, the gateway redirects them back to your site to the appropriate step in the checkout process. Hosted payment gateways are also called redirect payment gateways.
2. Self-hosted: Merchants collect payment information from customers on their site and send that data to the third-party payment gateway in the backend. The payment processing happens off-site.
3. Non-hosted: Merchant both collects and processes the payment on-site. Typically utilized by larger enterprises, as it requires a lot of technicality and maintenance.