I think this is known as a tankless water heater in the US. (Tankless because you said it's on the wall.)

Boilers in the UK are usually mounted on the inside of an exterior wall to provide for venting exhaust gases outside. They may provide hot water on-demand without a tank (combi boiler) or fill a hot water cylinder on a schedule (system boiler) depending on type. Heating is typically provided by the boiler pumping hot water through a circuit of wall-mounted radiators regulated by TRVs (Thermostatic Radiator Valves).

Boilers are definitely much more common in the UK than US. I believe New England is one of the few areas of the US that has a relatively high percentage of homes with hydronic+boiler heating setups. In most other parts of the U.S., many people probably have no idea what a boiler even is.

Pretty common in the Northwest part of the country as well.