I have noticed a few times that you equate exhaust air heat pumps with air heating. This is by no means the same. It is only meant as a hint because it can be quickly misunderstood and is not meant to start a fundamental discussion.
Guilty as charged.
The problem with exhaust air heat pumps is that they cannot supply external energy (apart from the electric auxiliary heater). That means the building must virtually not lose any heat energy, or even gain some passively, e.g. through solar input, for this type of heating to work. It becomes especially critical when the heat from the room air should also suffice. Because to achieve this (as if the perpetual motion machine of warming room air weren’t already difficult enough), it really requires passive houses, zero-energy houses or plus-energy houses. Therefore, no, of course an exhaust air heat pump is not an air heater per se, but when used in the wrong building (which seems to be more the rule than the exception, because the investment is cheap), it becomes one.
Now I don’t know exactly what you mean by "air heating." Commonly, the air-to-air heat pump is understood, meaning energy is taken from (indoor) air and transferred again to air. In my opinion, this is still burdened with the downside of comfort, because having warm air blown around your nose via a fan convector is unpleasant. A surface heating system is much more comfortable.