phase mod x freq mod equivalence
phase is the integral (w.r.t. time) of frequency.  and they are definitely not two independent processes.  back in, i dunno, the 30s, Armstrong implemented FM for the first time using AM and a synchronized carrier that was 90° out of phase with the AM.  so he was first accomplishing phase modulation (PM) out of AM (for which they had the existing technology - they didn't really have VCOs back in that day), then he implemented FM out of the PM by integrating the audio modulation signal and applying that to the PM modulation input.

this is all in a basic communications systems textbook like that of AB Carlson.