Language is a very versatile thing; and the meaning of words is a social convention, nothing more. So if two people agree in their conversation to call a ground-source heat pump geothermal, then it is, for them.
However, from what I've seen, it is more commonly the case that people call it geothermal as a mistake. Ground-source heat pumps are indeed solar ...
A ground-source heat pump is not a form of geothermal energy at all.
energy source is underground natural nuclear reactions;
source temperature is over 50°C;
Energy is extracted with passive heat exchangers.
Ground-source heat pumps:
energy source is solar radiation;
source temperature is about the same as annual average air temperature;
Yes, it is geothermal energy. From Wikipedia: Geothermal energy is thermal energy generated and stored in the Earth.
The entire point of in-ground heatpumps is to treat the ground as a large heatsink that's unaffected by weather, seasons, and the day-night cycle. These systems use pipes buried below the depth where the ground ever freezes, just like utility ...