A familiar example is a gasline engine that burns fuel/air. If the ignition is advanced, the mix too lean, or the octane's too low the mix will knock(detonate), because the pressure is high enough. The fuel/air instead of burning with a smooth flame front and providing an even push on the piston, explodes and bangs the piston really hard. The engine doesn't transfer any of the power to the wheels, because all the energy goes into wrecking the metal parts in the engine.
If the mix in the FAE bomb is ignited before it's dipersed, it will just burn like napalm, or a flung bucket of burning fuel. If it's allowed to mix with air beyond it's explosive limit, it will detonate. That's what generates the overpressures. One of the key ingredients in FAEs is cyclonite, it's in there by design to insure an explosive mix.
Incendiaries are used to start fires. With FAEs, there's a big fire, but the mix consumes all the oxygen in the area. For that reason it wouldn't be used to deliberately start a fire, because the things one wants to set fire to won't burn very well w/o the oxygen. Incendiaries other than napalm types usually contain powdered metal or phosphorus. Those additives raise the temp. quite high and spread burning pieces all around.