There is no fool-proof classification system for magicians, and no matter how hard we try to clarify the issue, the magicians themselves will continue to use the names that they have always used, as unconcerned about what the neighboring worlds do as ever. I have managed to gather some loose categories that seem common across several worlds, however. I have listed them below.
Beings Who Are Born with Magic
The two most powerful natural magicians are the mages and the sorcerers.
Mages normally have a single talent (and have no more than three). These talents range from psychic abilities (such as telepathy) to mere enhancements of mundane abilities (for example, the traditional super-strength). Where exactly natural humans leave off and mages begin is a matter of much debate. Mages occasionally use gestures or chants to help them focus, but the powers that they use do not originate from these. Also, the effects of their ability normally ends when the casting is finished.
Sorcerers tend to have more flashy abilities. They also have a wider range of abilities. It is common for them to use a focus to help control their powers. Sorcerers typically live in the country, away from crowds, and they are picky about whom they help.
Unnatural Magic Users
The two biggest groups in this category are the wizards and the technomages.
Wizards extract magic from plants and magical beings. They store the power in objects such as amulets, wands, and staffs, and with these objects they can cast lasting spells or give power to others. Wizards can either store the magic as a general power which can be used to perform any spell, or they can store it in preparation for a specific spell. Because the majority of preparation for such a spell is done when the powers are stored, the effort to enact the spell is relatively low; however, this limits the usefulness of the object to that spell.
Technomages are not actually magical users, but this is not apparent to anyone watching them work. They are a clan of highly advanced individuals who have merged with their technology. I myself am considered a technomage by most of the worlds that I visit because of my computers, guns, and cyborg implants, but there are others who are far more advanced than I. I have only met them a handful of times, and they never stay to chat. They are sojourners. It is my belief that their home world was destroyed, but this is simply because they don’t seem to have one.
Witches and Warlocks
This is probably the most poorly defined category. It acts as a catch-all for the minor magic users. Most of the users in this category use potions, chants, and diagrams to create their spells or curses. Although they often have a small amount of natural powers, they tend to use power in objects or other beings to enhance their own.
Although this is technically the correct name for anyone who uses magic, in practice it is more commonly used for prestidigitators who use illusions and slight of hand to imitate magic. Therefore, my suggestion is that you use the terms that your audience understands and forget about technical correctness.