wizard, mage, magician, those terms are really the same, in English writing, the author usually use different terms in the context to avoid repeating the words, and also, in some cases, different terms are used in different situation, for example, in a formal meeting, or in a guild concil hall, mage, magician are usually used, though wizard is used rather informally.
A person engaged in the above profession usually use 'spells' to achieve their goal, things like 'fire ball', 'Color Spary' etc, those who study the art of magicka DO NOT have to be a natrual born person with magic ablilities, they learn those skills rather than have them embedded in their own body.
In contrast, sorcerer or sorceress are born with magic ability, they do not have to learn or memorise spells to use them, rather than that, they can alter their surronding or object by mean concentration. I have a thread explaining those terms in more details, I will pump them, hope you can find them useful. Good luck.
P.S I dont think there are any sorcerer or sorceress in Krynn or Faerun, though I can be mistaken.