You probably want to specify the type of device you mean, then, since the term GPS generally refers to the technology and not any specific device.
Examples of two way GPS devices would be most new cell phones, the OnStar devices in cars, tracking systems in boats.
You're right that usually the handheld Geocacher type devices cannot send signals, they are antennas/processors only. The GPS devices in cars, though, are commonly two way. That's how they download updated maps if they have that capability and anything with a "subscription" service would have to be two way.
Radar is entirely different, a signal broadcast from the source and reflected back to the source, it doesn't depend on an external communication the way GPS does. Radar wouldn't help someone find you if you were the one with the radar.