Do the places you are referring to not require heat? If so I don't see why having a separate heating and cooling system would be cheaper to maintain than a single system. Come to think of it I don't see why a heatpump would be more expensive to maintain than split AC. I guess there is some extra circuitry to make sure it doesn't ice up in the winter and maybe backup resistance heating builtin.
"Heat pump" can mean many things, from essentially "split A/C" (air-air heat pumps) to ground-source heat pumps, using floor heating for the output, warm water production from the heat pump, etc.
But not all electric motors are paired such. Which is the point: a heat pump and an AC are "the same thing" at the gross level, but that doesn't mean all ACs have all the bits and bobs necessary for them to act as heat pumps.
I think they mean "air exchange" (split AC) vs "heat pump" (dig into the earth to draw/eliminate heat). Not saying that's the right definition though. I am guessing at an auto-correction of what they meant.
Dug into the ground, we usually call a "ground source heat pump", or less accurately, "geothermal". The normal split systems are "air source heat pumps". AC is a heat pump without a reversing valve.
A heat pump is not necessarily dug into the earth. Rather, the flow of the heat pump is moving heat (thermal energy) from outdoors to indoors or the other way around in an air conditioner.
Depending on the direction of the coolant flow, you get either a indoor heating or cooling unit. This is best demonstrated by going in front of the outdoor unit of a heat pump, when they are cooling, the outdoor unit generates heat because it's compressing gas, which then is then expanded when it reaches the indoor unit, generating cold. Exactly like a refridgerator.
it makes sense combined with solar, I think. Hot weather usually means a lot of solar energy you can ideally use to cool your home. I still wonder why there isn't as much PV activity in Greece. I see solar water heaters on nearly every roof, but not solar energy.