A coil is more like an Antenna than anything else.... It has transmit & receiver loops and not much of anything else..
Like AM or FM radio different antenna work better than others as they are "tuned" for frequency. Metal detectors of similar frequency can use similar coils.... Beyond that you can have VERY different machines with all kinds of circuits for different modes & filters but they can have the same Transmit/Receive coils....
So, while the COIL may be identical, the machines may be far different from each other in how they process the info. Since most hobby machines run around they same frequency the coils are mostly the same design, BUT!!!! the way they are wired or the pin configuration may not let them just interchange "Plug & Play" style, But if you can find the correct leads, It is as simple as hooking up 2 antennas. One Transmit Coil Lead, One Receiver coil lead & perhaps a ground makes the other 2 connections, but may be 2 wires per loop PLUS a ground to reduce interference. I had a link to a site with a torn down coil showing guts, but cannot find right now...
The bottom line is. Coils are simply two antennas, tuned to frequency range(s) of the transmitter or the receiver. DOC