Hydrogen electrolyzer is apparently the correct name however I feel if something is to be named for what they do then because these make a usable fuel I prefer to call them fuel cells where as a conventional 'fuel cell' is a device that hydrogen and oxygen is pumped into making electricity and water. Also not to be too confusing, a gasoline container used on a race car is also called a fuel cell where as the container that does the exact same thing on your family car is called a gas tank.

In  any case what these pages are about is a unit that holds water and is subjected to an electrical current which separates the hydrogen and the oxygen from water. The gases are then collected and burned as fuel.

This photo is the working area of a current design I'm playing with.