What makes a wizard different from an enchanter, a magician, a sorcerer, a thaumaturgist, etc. Well, sorcerers are sometimes evil, "black magicians" (i.e., practitioners of black magic), but in general, not a lot, although fantasy authors and FRPGs might use the names with narrower meanings.
For example, Dungeons & Dragons Third Edition (D&D3E), distinguishes between sorcerers and wizards:
Another example: "The difference between a wizard and a sorcerer is comparable to that between, say, a lion and a tiger, but wizards are acutely status-conscious, and to them, it's more like the difference between a lion and a dead kitten." (Steve Pemberton, The Life & Times of Lucifer Jones)
Lyndon Hardy's Master of the Five Magics suggests ascending ranks of thaumaturgist, alchemist, magician, sorcerer, and wizard.
Famous wizards in folklore and fantasy fiction (sometimes both) include: