Semi, No. It is only the Class D amplifier that uses power FET's as pure switches like you said, thus drastically reducing power consumption and heat generation. Those designs are often used in the built-in subwoofer power amps and car audio, where a compact but extremely high-power amplifier is desirable.
An analog FET power stage (Class A or AB) uses the FET's more like a pair of "variable resistor" or "volume control" connected in serial between the power-supply rails. The source/drain resistance is controlled by the gate voltage. The gates of the "top" and "bottom" power FET's are driven out-of-phase, swinging them in the opposite direction according to the input signal. So, the FET power stage actually behaves much like a push-pull tube amp (hence chess's misunderstanding), but still having a very low output impedance just like the usual (bipolar) solidstate power stage. I remember that when the FET power amp started to appear in the consumer audio market in the early 70's, it was advertised as having "the best of both worlds" (meaning, the benefits of both tube and solidstate). Today, many manufacturers seem to stick to either bipolar or FET, while a few companies do use both technologies mixed in their lineup. But I have not closely followed up their pros/cons lately, and so got curious...
