My air heater was a 5.5Kw output with an input of something silly like 2.1Kw Basically they work like a fridge in reverse by drawing the cool air in from outside and using it to heat the water from the pool as it passes through a series of coils. Never really went through the intricacies of it, was just made up when my electricity bill dropped like a stone.
We have one of these to heat our conservatory, rather than radiators (apparently, due to the amount of glazing, CH wouldn't put heat in quick enough to negate the losses, meaning it would not actually get any warmer!) It will cool the conservatory as well, but we only use it in heating cycle. Supposedly, it is pretty cheap to run in that mode.
Yes, they work like fridges-in-reverse. The outside unit draws atmospheric air through it, and whatever heat is in that air "warms" the circulating "refrigerant". The refrigerant (now with added heat energy) is circulated to the internal (wall-mounted) unit - a bit like a storage heater - where it is compressed, and the heat energy released. Warmer-than-outside air is then blown into the conservatory.
The refrigerant is pumped back outside, where it decompresses, and therefore becomes pretty cold), where it scavenges the latent heat from the outside air again. Rinse and repeat, until you switch it off.
Because of the heating effect of compression, the air that is blown into the conservatory can be considerably warmer than that outside. IIRC, an outside temperature of zero degrees C can still be compressed to give low twenties degrees C air inside.
Obviously, it takes a lot more energy to warm a given mass of water than the same of air, so any heater will draw more energy and take longer to heat a pool than it will a conservatory. Conversely though, it takes longer for that mass of water to cool back to "ambient" temperature.
