Those types of heat pumps you describe are pretty rare actually. They are called ground source heat pumps and you need to have lots of pipes buried all over your garden (or alternatively bore down). Very good but very expensive so you don't see them very often as you need a big garden and wallet. There's another similar type heat pump where you throw the pipes into a body of water. A lake on your property would be ideal but I've never seen one in the flesh as I stay away from those types of people.
The most common type of heat pump in these isles is an air-to-water heat pump. This transfers heat from the air to water (unsurprisingly) which gets pumped around your rads. You can retrofit this to your current system usually. I'm guessing what
@Kandi1977 has is a split air-to-air system. These have units up on the wall or ceiling which blow hot air in (or cold in the summer).
Heat pumps will be everywhere at some point in the future but there are a few hurdles. One is that they are not cheap to buy at the moment (air to air is not bad actually) but they will drop like everything else over time so that will solve itself. Problem two is they only work efficiently in well-insulated and relatively airtight houses. I check that houses meet the minimum criteria for the government to pay out a grant for their installation. If the house is not up to spec the heat pump will be working as hard as a victorian child all day long and cost too much to run.
The heat exchanger idea you describe is called heat recovery ventilation which is a little different. You can get these as small units to replace your wall vents, or a more sophisticated MHRV system with ducts running to each room (hard to retrofit). There are few other systems that are halfway between these extremes. As you say, they recover some amount of the heat from the air being exhausted so you are not pumping all your money away.