The electric boiler : electric resistances immersed in water produce heat. Once heated, the water is sent to the central heating system, then to the radiators or underfloor heating. The latter will then transmit the heat to all the rooms. More economical to buy and to use. No maintenance required.
The gas boiler : the combustion of natural gas or propane heats the water through a heat exchanger. More powerful and can produce domestic hot water. More expensive to buy and requires annual maintenance