The difference between a boiler and a hot water tank has to do with the way in which each uses the hot water that it produces.
Both boilers and hot water tanks take cool water, heat this water and then distribute it throughout a home via pipes. However, the water that is heated by a boiler is distributed throughout the home via pipes, radiators and radiant in-floor systems in order to heat it – to keep the rooms, floors, garage, etc. comfortable and warm.
On the other hand, a hot water tank heats water that is used for cooking and cleaning purposes – for showers, dishwashing, laundry, etc.