"Frequency modulation" as a term usually means phase modulation. Yamaha called all their phase modulating synthesizers "FM".
There is a difference between Chowning's original "frequency modulation" idea, and phase modulation, but PM for sound synthesis is very practical to implement and actual frequency modulation is not. (It's practical for other purposes, like radio, though.)
So, fundamentally I must disagree without opening statement. "Frequency modulation" has TWO meanings in different contexts, and one of those is actually "phase modulation". It is correct that one of these two meanings does make a distinction between them, but in the world of sound synthesis FM is PM.
As mad was mentioning, at least for some ideal cases you can provably produce exactly the same waveform result with both. In practical implementations for sound synthesis, though, it is very important to have control over the relative phase of both operators continuously, and this just isn't easy to do with true modulation of frequency. As soon as the phases slip between the two, the sound changes drastically. Phase modulation, on the other hand, puts it directly under control, very simple, and very stable.
This is the same reason that "frequency modulation" on the FDS is hard to use for that purpose. It's actually modulating the frequency, because it was intended for use only as vibrato, not as a waveform synthesis technique. When you put it up to high frequencies, there is not enough numerical stability, and the phase between your modulator and carrier is constantly slipping. Like you can sorta do FM sounds with it if you can live with them also having a constant "phaser" effect on top, and some detuning.