When arriving at JFK (or any US airport) on an international flight that didn't have pre-clearance, I know that you have to clear immigration, collect your bags, clear customs, re-drop bags, change terminals by AirTrain if needed, and then go through security, no matter what terminals are involved.
I also know that when you fly into JFK on a domestic or pre-cleared flight, and your onward flight is from that same terminal, you just step off your domestic flight into the departures area and walk to your onward gate, without needing to do security again.
At some other big US airports I've been to before (eg DFW), there is an airside transfer train that lets you move between terminals, so you can go from gate to gate without needing to exit + re-clear security. However, at JFK the only transfer train I'm aware of is AirTrain, which is landside.
Is it possible to move between terminals at JFK from within the airside / departures area? Or is the only option when changing between domestic flights at different terminals to exit, take the air-train, then queue up and re-clear security?