Is it true that frequency deviation over 2*pi is the phase deviation of an FM/PM signal?
An angle modulated signal can be described as either phase modulated or frequency modulated.

The modulation index is the phase deviation in radians of an angle modulated signal.

The modulation index at a single modulation frequency is \$\frac{FrequencyDeviation}{ModulationFrequency}\$

Both the modulation index and the frequency deviation are measured as the peak deviation.

Both the frequency deviation and the modulation frequency are measured in the same units, that is they are both in Hz, or radians/s.