You two are referring to the 2.4 ghz wifi signal which provides FPV and telemetry.
This stuff is proprietary, but it's been discussed on this site for over three years now and this is my understanding from reading hundreds of threads on here since I joined.
The 5.8 is easy. Controller sends, bird receives. Done.
The 2.4 is a whole different story.
There is no "video receiver antenna" or "video transmitter." Both the controller and the P3S have two transceivers with an antenna connected to each. Each is the same, but they switch between each other automatically in an constant effort to get the best connection. But that's just the beginning.
It's a very complex process which allows the system to work. For example, in order to see video on your mobile device, the bird must transmit, the controller must receive, the controller sends data back to the bird called a check sum. The bird then receives the check sum and sends yet more data back to the controller to verify whether the data sent the first time is correct, and then, finally, if the data is correct, the controller sends the data to the mobile device on yet another 2.4 frequency (and this whole check sum process may very well go again between the mobile device and controller).
Hence, the need for a two-way amp. The Sunhans is a two-way amp.
Both antennas do the same exact job, so it doesn't matter which antenna or transceiver you connect the amp. And that's also why many if not most pilots use just one amp for 2.4. The switching will prefer the best connection which would be the one with the amp.
People have experimented with putting amps on the bird but it hasn't shown any better connection than with the amp on the controller.
Apparently putting amps on both doesn't work any better than one amp on one or the other, and often works worse.
The amp on the controller amplifies the incoming signal kind of like a hearing aid amplifies a sound wave. Yes, it can amplify noise too, so you'd want a directional antenna and you'd want to aim it correctly to minimize the noise and maximize the desired signal.
Hope this helps.