Don’t all heaters (except infrared) heat with warm air? A convection radiator also warms the air, just without a fan.
That's right, it's always about warming the room air so that living beings feel warm. Air is - as you pointed out except in the case of infrared - what is ultimately heated.
An air conditioner is perceived as unpleasant because of the "draft." Underfloor heating is considered comfortable due to the good distribution without hotspots. Radiators and stoves just warm a corner because the air is not stirred.
The effect is the same, though; it's about getting warm indoor air.
You can also warm up with a campfire. But it feels different then. In this respect, was absolutely right that underfloor heating cannot be compared to air conditioning. There is a reason why this type of heat pump heating has not established itself (not to mention the poorer performance in winter).