Transparent Proxy
Transparent proxies don't hide, or mask, your real IP in any way. In RFC 2616 the standard definition is: "A 'transparent proxy' is a proxy that does not modify the request or response beyond what is required for proxy authentication and identification". and "A 'non-transparent proxy' is a proxy that modifies the request or response in order to provide some added service to the user agent, such as group annotation services, media type transformation, protocol reduction, or anonymity filtering".
Gateway: Sometimes called a tunneling, or transparent, proxy
A gateway is a proxy server that passes all requests and replies unchanged.