Heat pumps here heat water. In a new build with a heat pump from the start, or a big refurb, the hot water is used for underfloor heating. In a smaller refurb, or where that's not possible, it's used in radiators, although I think you typically fit special radiators and bigger pipes which can work at a lower temperature.

Some new builds have mechanical ventilation heat recovery, which is a ventilation system with a heat exchanger. But I don't hear much about air to air heat pumps.

It's very possible I'm wrong in my perceptions here!