How to express FM and PM the most simple way?
In the simplest terms, the difference between analog Phase Modulation (PM) and Frequency Modulation (FM) can be defined according to which of the two (phase or frequency) is being directly proportional to the message signal as outlined by the following:

An angle modulated signal is defined as: $$x(t) = A_c\cos(\omega_c t + \phi(t)) $$ Where $\theta(t) = \omega_c t + \phi(t) $ is the instantaneous angle  of the modulated cosine, $\phi(t)$ is the instantaneous phase and  $ \omega_i = \frac {d\theta(t)}{dt} $ is the instantaneous frequency

Now consider the phase being given by $\phi(t) = K_p m(t)$ , where $m(t)$ is the message signal and $K_p$ is a simple constant for phase modulation. As clearly evident, here the Instantaneous Phase, $\phi(t)$, is directly proportional to the amplitude of the message signal $m(t)$ and hence this type of angle modulation is called as Phase Modulation (PM)

On the other hand, consider a message signal $m(t)$ such that $\phi(t) = K_f \int {m(\tau)d\tau}$, where $K_f$ is the constant for frequency modulation, then the instantaneous frequency is: $$ \omega_i = \frac {d\theta(t)}{dt} = \omega_c + K_f m(t) $$
As can bee seen, now instead, the instantaneous frequency in radians is directly proportional to the amplitude of the message signal $m(t)$ and this type of modulation is, therefore, called as Frequency Modulation (FM)