At least in North America, the term "Air conditioner" means a device designed to cool a room, where a "heat pump" can cool or heat that room. They work by the same exact principle (all the compressing, condensing, evaporating stuff) but a "heat pump" has a method of running in both directions. You could probably contrive one that could run the pump in either direction but I think most use a valve to switch which is the high pressure/hot side and which is the low pressure/cold side.

I grew up in a house with a heat pump, I currently live in one with an air conditioner and a furnace. When it's time to replace my air conditioner (or do other heavy maintenance to the system) I'm going to look into a heat pump, with the furnace as a backup heater in lieu of strips.