The characteristic difference between a phase modulator and a frequency modulator is:

Phase modulation (PM) and frequency modulation (FM) are very closely related forms of angle modulation. The primary mathematical difference between them is how they respond to the frequency of the modulating audio signal. In a phase modulator, the amount of phase shift is directly proportional to the audio amplitude. Because of how phase relates to frequency, this naturally causes the equivalent frequency deviation to increase as the audio frequency increases. To make a phase modulator produce a flat FM response (indirect FM), the audio must be processed through an integrator (rolling off higher frequencies). Conversely, applying pre-emphasis to a standard FM modulator makes it mimic phase modulation. Therefore, the characteristic difference in the audio processing chain between how these two modulators handle audio is the use of pre-emphasis (or its inverse) to tailor the frequency response. Options like frequency inversion or centre frequency do not fundamentally distinguish the two modulation methods.