Both move heat rather than generate it. The difference lies in how that heat is delivered.
Air-to-water
Heats water for underfloor heating or radiators, and also provides your domestic hot water. It replaces your boiler, but needs a well-insulated home and a low flow temperature.
Air-to-air
Blows warm or cool air straight into the room. That's what most people call air conditioning. Ideal for a single room, and more economical than heating with electric radiators.
If you're torn between the two, the conversation starts with your insulation, not with the device.