For larger homes with central heating and radiators inverter air conditioners aren't really a great solution - they are expensive (especially when you don't have/need an air conditioner in the first place), unsightly and work for more or less just one room. A heat pump is a generic term for a multitude of things, but as a replacement for central heating you'd most likely have just one outdoor unit that spews cold air and inside you'd have a large heat exchanger where you warm up the water for your central heating (and possibly warm water in general for showering and the like).

It's pretty amazing.