A one-piece toilet is a style of the toilet where the tank or cistern is connected directly to the bowl, so it is one full unit, whereas a two-piece toilet is made up of two separate units, which are then joined.
A wall-hung toilet is a system in which the toilet bowl is mounted directly to the wall, while its tank is installed inside the wall. This allows wall-hung toilets to take up less space. Having the tank behind the wall gives a more modern look since the working parts are hidden.