Switch has two positions, on or off. The switch can be changed within the events of the game. RPG Maker will keep track on the position of the switch throughout the game. More than one switch can be in use at the same time.
Variables act similar to switch, but dim, rather than two distinct positions (on or off). With variables, you do not have a limitation, rather an unlimited amount of positions.
You can also think of it this way. A switch identifies if the treasure chest is open or closed. A variable provides the amount of coins inside.