"Ordinary" frequency shift keying is what happens if you make a transmitter toggle between two frequencies. It turns out that because a single sideband transmitter is basically an image-rejecting upconverter from audio to RF, if you feed FSK at audio frequency in an SSB ham rig, you get FSK at RF, just like the FSK you'd get from a dedicated FSK radio (at least if the frequency shift, mark/space polarity, baud, and word encoding match)
But the situation with an FM transmitter is different. There, to get the carrier to toggle between two frequencies you would have to instead inject a toggling between DC levels into the FM modulator, almost as if you just wired a serial port up to the FM modulator input.
If instead, you feed audio frequency FSK into an FM transmitter, you get something different, effectively AFSK-over-FM. Given that there were some surplus FSK solutions around (not the ones used on everyday telephone lines, but rather ones which needed leased line bandwidth) hams started rigging these up to plain or only slightly modified FM voice gear and building interconnected data networks.
The two are fundamentally different and not compatible. To demodulate ham VHF packet, you need to first demodulate FM audio, and then demodulate the audio frequency FSK - but there are many solutions for each, easily chained together.
It does seem vaguely possible that by feeding an alternating stream of 1's and 0's into an FSK radio with the right shift setting, you could create an audio tone in an FM receiver. And then if you changed your baud rate (or changed your pattern to toggle at a different bit interval) you could make the audio tone change to a different frequency. So there may be combinations that work, but you'd have to spend some time playing with the numbers and they might not be within useful range. You'd also have something of a problem in that you'd be using a square wave as your audio waveform, at least to the degree that such got through the filters. And of course you'd need the transmitter's FSK deviation to be compatible with the FM receivers. Almost interesting enough to try it in a closed system...