Class A :: Each transistor conducts a DC-current which is never cut off during the AC cycle. One (or each) transistor controls the full AC-period.
No crossover at zero crossings.

Class B : No DC-current, Each transistor controls exact half of the AC-period.
Maximum crossover distortion.

Class AB : Compromise between A and B: Opposite transistor is (gradually) cut off at small output current.
Small DC-current for limiting output impedance at zero crossings.

Class C : 1 or 2 transistors are switched on during part (till 50%) of the period.
Only usable for output-power at switching frequency at fixed amplitude. Load is resonator at switching frequency. Capacitive load at harmonics create switching losses.

Class D : Like Class E (or C), but with symmetrical or push-pull output and filter for rejecting the switching frequency.
PWM (Puls Width Modulation) generates linear output power at a bandwidth till 1/5 of the switching frequency. Load is inductive at switching frequency and harmonics.

Class E : Switching transistor(s) with reduced switching loss by ZVS (Zero Voltage Switching).
Filter is tuned at switching frequency, with open impedance at all harmonics.

Class F: Like Class E, with filter tuned at harmonics of switching frequency, with open impedance at 3rth harmonic for F3 etc.
Class E and F are like C only usable at small bandwidth and constant amplitude (defined by supply voltage).

Class G : A Class B or AB amplifier where the supply voltage is continuously regulated by the amplitude of the output signal, to reduce voltage dissipation in output transistors.

Class H : Like Class G, Supply voltage is switched between 2 (or more) levels, depending on output voltage.
Maximum voltage dissipation is 1/2 (or less) compared to Class AB