I'm actually studying for my general ham radio license right now! Most FM receivers use something called a "mixer" to modulate the frequency to a known constant, then they use a circuit called a "discriminator" or "quadrature", both of which are "detectors".

Typically they're not measuring the frequency or phase itself, but rather the change in frequency or phase.

Edit: I should note that's only for analog circuits. DSP is also common.