Each box contains a special power inside it and can only be activated by one of the rings worn by the rings pertaining to their elements (sky, sun, cloud, storm, rain, lightning, mist) The power inside each box runs off of the elemental energy of the user.
Most boxes are different, very few have replicas as you will see as you continue on through the series.
Also the boxes are not restricted to one person. As long as someone has the elemental power to use it they can. (ie Gamma could use the same ring as Lambo)