Old style residential heat pumps do indeed have resistance strips or a backup gas burner. In fact the whole system is usually centered around a standard electric or gas furnace. The heat pump condenser coil is just inline with the air fed from the furnace. When the outdoor coils are operated in a damp environment, the coils will begin to ice up due to the moisture in the cool damp outside air hitting the cold evaporator coils. The heat pump can sense this, and operates a reversing valve reversing the flow of refrigerant. This heats up the outside coils and cools down the inside coils. the resistance strips come on so that the occupants of the home remain comfortable and don't experience a blast of freezing air from the ductwork. The ice melts off and falls away. Then the system reverts back to a heat pump. You can turn off the strip heaters and the system will still function, but you will feel that cold blast and the deice cycle will last longer.
More modern systems, (ductless mini splits) do not have resistance strips. It just turns off the inside fan and just lets the waste heat of the compressor heat the outside coils, therefore the deice cycle takes longer, and all you feel is a lack of heat, just like the system is off.
I have no idea how the leaf system works, but I'd bet its more like the second system than the first.