Some are Piston others are diaphragm design each can type can be environmentally sealed which is to keep the internals clean and helps performance in cold water by reducing icing.
The first stage is to reduce the pressure in the tank to a level that the second stage can handle.
It has to deal with the tank pressure reducing from consumption during the course of the dive and maintain consistent pressure regardless of this fact and the external pressure changes from different depths.
The second stage reduces the pressure further to a level we like to breath and some are adjustable for effort of breathing. They are demand valves and shouldn’t flow without being sucked on. Some have means of avoiding free flow at the surface with a sort of switch that can partially obstruct the venturi