FPM is a process manager to manage the FastCGI SAPI (Server API) in PHP.
Basically, it replaces the need for something like SpawnFCGI. It spawns the FastCGI children adaptively (meaning launching more if the current load requires it).
Otherwise, there's not much operating difference between it and FastCGI (The request pipeline from start of request to end is the same). It's just there to make implementing it easier.