A split system AC is a heat pump in any context. So is a refrigerator. They're all the same technology that move energy via a refrigerant's latent heat by compressing it into a warm part and letting it expand into a cold part.
I like "heat pump". It's a very nice ELI5 name. It's a pump for heat. A water pump takes water and forces it to where it wouldn't go naturally. A heat pump does the same.
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).