Mechanical engineer here!
What the OP is referring to as "Efficiency" is what's known in the industry as COP (coefficient of performance).
A system's COP is equal to the amount of useful heat energy supplied or removed by the system divided by the amount of energy used to do that work.
If your heat pump uses 10 Joules of electrical energy to move 40 Joules of heat energy from the outside into your house, that heat pump is operating at a COP of 4 (or 400%).
Only heat pumps can have a COP of >1, due to conservation of energy. A traditional gas or electric heater uses combustion or electrical resistance to lossily convert electrical or chemical energy into heat energy.
If everyone in the world had an engineering degree the distinction might have been important, but complaining about it in this context is just pedantic.