Why A frequency discriminator is the classic FM demodulator: a tuned phase-shift network (as in the Foster-Seeley discriminator or ratio detector) converts instantaneous frequency deviation into a proportional amplitude, which is then rectified to recover the audio. Its S-shaped response curve gives zero output at center frequency and positive or negative output as the carrier swings above or below it. Modern receivers often use a quadrature detector or PLL for the same job, but the discriminator is the named textbook circuit.
Watch out The choice calling it an FM generator has it backwards: creating FM is the job of a reactance modulator or a directly modulated VCO, while the discriminator is on the receive side.
Discriminator DEtects, it tells frequencies apart on the receive end; reactance modulator makes FM.