With AM, the frequency of the carrier is fixed and the modulating signal controls carrier amplitude.

With FM, the amplitude of the carrier is kept constant and its frequency varied by the modulating signal.
This variation in carrier frequency is called DEVIATION.
The amount that the carrier deviates in frequency is proportional to the loudness of the Audio modulating signal.
If you shout into the microphone, it deviates more than if you whisper.
Deviation is expressed in kHz per Volt. The BBC uses 15 kHz/Volt.
The maximum deviation allowed by the BBC is plus and minus 75 kHz from the carrier frequency.

How often the carrier deviates is determined by the frequency of the modulating audio.
If you whistle it deviates more frequently than if you hum into the microphone.

Since FM signals occupy a wide bandwidth there is no room for them on LW or MW.
They use the FM band of 88-108 MHz where there is plenty of band space available.

Advantages of FM are higher quality and low noise.