Pure physics-wise, you are correct. Heating the same volume the same amount requires the same amount of heat energy. The difference is the source of the heat energy.
A resistive heater produces the heat by consuming electrical power only, 3400 BTU/hr generated heat requires a bit over 4.2A of 220V electricity to flow through the resistive element. (specs from a Radiant Cove heater unit)
A quick intro to the refrigeration cycle can be found here https://www.swtc.edu/ag_power/air_conditioning/lecture/basic_cycle.htm.
A heat pump is the same as an air conditioner or fridge, just installed with the condensor inside the building and the evaporator outside. The primary heat source is the outside air and the only power is that needed to power the compressor unit to move the working fluid through the cycle. The smallest Fujitsu unit generates 11000 BTU/hr using 3.7A at 220V.
Basically the answer is the same amount of energy is needed for the same heating, but the heat pump uses a different source and an efficient process to produce the heat than a resistive load does.