@FolornLawn that's an air-source heat collector and heat pump in the BBC article. It has a fan which pulls air across the heat exchanger. The heat exchanger is like a reverse fridge and sucks the heat out of the air, and
condenses it into a much smaller volume of liquid.
Ground-source heat collectors are usually pipes buried in loops under a field, or in vertical wells below ground. The heat is collected in a fluid then passed through a heat pump. The heat pump is above-ground and would be like the air-source picture but minus the big fan, so more compact.
The temperature under the ground is much more stable than the air temperature overground, so in cold climates, it's worth going to the extra expense of drilling a well, or digging trenches to put the heat collector pipes into. This is because in the coldest part of the year, you can draw on the heat stored in the ground. In milder climate places, it's a less clear-cut choice. In very cold snaps, you'll just be using an air system like a regular electric heater, but if there are only cold snaps every 5 or 10 years, that might be ok, as it will still be cheaper over, say, 15 years to install and run an air system compared to a ground system.
The time it takes to get to the same installation and running cost point is called the 'payback' time. So it's cheaper to install air systems, but more expensive to run (compared to ground systems). In cold climates, you get to the cross-over point quicker, as running costs are higher for air systems as they are not as efficient as ground systems.
Both systems need a well-insulated and draught-free house at a minimum, as they are not high temperature like piping-hot rads, or an open fire or log burner.
I think overall they are a good idea, but a rush to install them without proper consideration is a crap idea. Subsidised roof and wall insulation and double glazing of all properties would probably be better in the first instance.