Re: Whats the difference?
Depends on the game.
Conceptually they are essentially the same thing. But if the needs arises, those names can be used to identify different characteristics of magic wielders. In AD&D, a sorcerer is a raw magician. He draws magical power from himself. A Wizard is a thaumaturge, a student of the arcane arts. Magic is achieved through study. A Mage (which doesn't exist anymore on the recent versions, if I recall correctly) was the name chosen for pure magic wielder class before the game introduced different magic wielder classes in the 3rd Edition.
In Diablo, The Sorceress was an elemental magic wielder. Her skill trees were based on the elements of fire, cold and electricity (of those just one is an element, but you get the point). The wizard which will debut in D3 will instead focus on a more pure concept of magic in which elements don't dominate, but instead the concept of magical arts.