Space heater in the US refers to something different.

Home heating may be done using steam in radiators. As far as I'm aware this is most common in older buildings or in the north. New York has district heating that seems to resemble district heating found in parts of Europe.

A space heater in the US is a resistive electrical heater, that isn't usually connected to the main heating system for the home. Typically these are small portable units, and they're used to heat just the room they're put in. Your thermostat might control several rooms, but you might not intend to be in those, and night not want to pay to heat all of them. Or it's unusually cold, so you use a space heater and just stay in that room.

Different in australia too. Places with warmer climes tend to seperate these things.

I know why, but i'm still surprised at the dearth of reverse cycle outside of Australia. Incredibly ubiquitous here.

That used to be more common in the us. However forced air is more efficient (at least traditionally, not sure what the latest is) and most importantly allows for cooling which is needed when the summer gets as warm as the us normally does.

Hot water heat is extremely common in the Northeast US, at least. Not universal, but very common. It circulates separately from the drinking water but is heated by the same machine.

Radiative heating is (relatively) common in the US too, although not so much in new builds.