There's at least three types of heat pumps:
- air-air heat pumps which function like "inverted" AC, which is what you were thinking of - another quirk being that in some models the air vents have optional electric heating which provides more instant more intense heat at the cost of massive energy use
- air-water heat pumps which use air to heat up water similarly to a conventional boiler - a noteworthy difference is that they usually target 40°C instead of 60°C but like other heat pumps they're very energy efficient and are typically used with floor heating
- brine-water heat pumps which use brine running through underground pipes to heat up water similar to air-water heat pumps - these are arguably more efficient but more expensive to install due to the excavation necessary to lay the heat exchange pipes
The latter can further be categorized based on the layout of the underground pipes (YMMV on the exact nomenclature as English is not my native language):
- area collectors use a horizontal grid requiring a large area of land and limiting its use for things like trees or swimming pools (or anything that needs to go deeper)
- trench collectors use a vertical grid, essentially turning the area collector on its side - these of course require much deeper excavation but have a much narrower footprint but depending on where you live you may need to get additional permits
- basket collectors use a three-dimensional grid, usually split across a number of "cages" or "baskets" combining the footprint advantage of a trench collector with the depth advantage of an area collector
In Germany air-air heat pumps are the default with many prefab construction companies due to the ease of installation. When we built our house with a conventional construction company we went with a water-air heat pump because that's what the plumbing company was most experienced with. A brine-water heat pump would have been a good option due to the soil consistency and ground water level but sadly national regulations enforced a minimum depth much lower than what would have been otherwise possible and this made the option cost prohibitive for us.
The main advantage of air-air heat pumps is that they can be better used for cooling (because at the end of the day it's literally just AC) whereas other heat pumps are usually capped by the dew point to avoid condensation.