Frequency modulation and phase modulation are physically equivalent.
Suppose you have unmodulated sinusoidal signal, ew t
This signal has the phase of
phi(t) = w t,
and frequency of
f(t) = 1/(2 pi) * dphi/dt = w/(2 pi) = f0.
Now we apply the frequency modulation with frequency deviation of df and modulation frequency of fm:
f(t) = f0 + df Cos(2 pi fm t)
phi(t) = Integrate[f(t) dt] = w t + df/fm * Sin(2 pi fm t)
Now think about the phase modulation with modulation depth of m and modulation frequency of fm:
This means that the effect of FM is the same as that of PM. This indicates that the modulation depth of FM is given by
m = df / fm.
For given df, FM gives a larger modulation depth with a lower modulation frequency.