JP-1 was mostly gasoline and JP-4 is mostly Naptha which is close to gasoline. Jet A, A-1 & JP-8, K-1, etc. are a higher density distillate skimed off at a higher/narrower temperature.

On the full size engines, it's a matter of a fuel control adjustment and tolerance to higher operating temps. When I was flying Air Force OV-10's the ground school guys were careful to point out the screwdriver adjustment on the fuel control (accessable in the wheel well) where you could set it for the fuel you were using. Just needed to be aware the different operating limitations.

Nobody uses off nominal fuels these days since the normal stuff is widely available and there's little testing for such. Even the US Army went to a single fuel for all its vehicles - ground & air. But it could be done in an emergency. As for our turbines, I doubt it since the metering for startup and running is really only setup for the vaporization characteristics of standard jet fuel.