Think about this:
How does the discriminator in an FM demodulator work? What happens on the output of the discriminator when the received station is off ±frequency?
The FM detector produces a DC voltage when the radio is tuned away from the center of the station. The DC voltage corrects the frequency of the voltage-controlled local oscillator.
It is that simple.
Cheap FM radios drift their tuning so they use AFC to correct it. Good FM radios do not drift and do not need AFC.
Automatic-Frequency-Control.
When you tune toward a station then the AFC circuit snaps the tuning toward the center of the station's frequency. When you tune away then it seems like the station's frequency is very wide then it snaps away.
Manufacturers of cheap radios use AFC because the frequency of the cheap radios drifts. They blame the drifting on the stations. But stations are crystal controlled and do not drift.