How many different types of AC systems can be found on vehicles?

For the purposes of the A/C system recharging procedure, the important differences are those relating to the type of refrigerant (R134a/HFO1234yf) and/or to the type of compressor (electric in hybrid / electric cars, mechanical on other cars). The differences between compressor types (variable / fixed compressor displacement) or the type of system (with expansion valve / orifice) do not affect the service procedure.