Numerous different terms are used to describe magic users, most of whom will be very offended if you use the wrong one.
Mage Wars Era naming conventions are always confusing, and it's just gotten worse since then. Attempts during the second and third Ages to academize or socialize the practice of magic only added to the confusion. Typically, the Mage-Wars-Era conventions still stand.
'Wizard' is a strictly masculine term. This does not speak to any gender differences in magic itself or the use and teaching thereof. 'Mage' is the gender-nuetral term for a magic-user; 'wizard' is masculine; and 'sorceress' is feminine.
It is believed this distinction evolved during the Mage Wars as a result of the Marcon Alliance, who firmly maintained, despite evidence to the contrary, that "women couldn't do magic". Though all other aspects of the Marcons have been erased, the distinction survives of 'wizard' as a masculine term.
Wizard vs. Sorcerer
The wizard/sorceress distinction gets really confusing when one understands that a sorcerer (the masculine for sorceress) is not the same thing as a wizard. A sorceress might practice the exact same forms of magic as a wizard and be functionally identical, but a sorcerer is an entirely different thing altogether.
A sorcerer is typically much more powerful alone than a wizard, usually as a result of great innate abilities. Sorcerers more typically work alone and are more likely to employ complex spells. They are also typically practitioners of ritual magic, though many wizards also use spells in that category.
There is no direct term for a female sorcerer; she is still called a sorceress whether she is using wizard magic or sorcerer-style powers. Sorcerers are, in general, much more powerful than wizards. Stories from the First Chaotic Period tell of sorcerers who, alone, were able to take on entire towers.
Mages by Ability level
Within the tower system, you get different ranks and levels according to power. Exactly how these ranks are handed out varies tremendously from tower to tower, and it was considered bad form to use the distinctions outside the tower during the Mage Wars.
Afterward, as historians began copying and translating the various records from the Wars, it became common to refer to historical mages by their tower rank. Since Mage Towers vanished with the end of the war, no new mages gained such titles.
The first level of distinction was the 'Arch' prefix; this could be applied either to a wizard ('Arch Wizard') or a sorceress ('Arch Sorceress'). Because it was specifically a tower rank it was never applied to the sorcerer (thus there is no 'Arch Sorcerer').
The origin of the term Arch Mage comes from High Tower and the Asysias city-state. The state was both ruled and defended by a family of powerful mages. The head of the family, because he bore the weight of responsibility, was referred to as "The Arch" from the architectural load-bearing structure.
'Magus' was a gender-nuetral term and not applied as a prefix or suffix. A mage of that rank was simply identified as a Magus be they he or she. Some towers also used the sub-rank 'Megus' for a mage more powerful than a Magus but not quite powerful enough for the next rank. 'Megus' was not commonly used and is known only by written accounts from the Dynastic Period.
Though now regarded as a gender-nuetral title, most historians agree that it was actually a masculine term for which there is no feminine equivalant. Some historians argue that 'Megus' was the feminine term, though records cannot confirm or deny this. Surviving tower records that list ranks do not go into detail about the genders of the holders, and no biographical information on a mage with the rank of Megus list whether or not the holder was male or female.
Also a gender-nuetral (or masculine only, depending on interpretation of history), the Arch Magus is the lord of the tower, the highest-ranking (most powerful) wizard in a given Mage Tower.
Many other types of mages exist, though these do not correspond directly to any tower-ranks.
The Battling Sorcerers were some of the most feared mages of the Mage Wars. These were not tower wizards, but went into battle with troops. Most often they fought with only magic, though many were known to be capable warriors in their own right.
A Mageblade is a specific type of battling sorcerer who uses sword techniques to produce spellforms and cast spells. The term originates with Kosta Guitain of the Wizard Breakers, though he is not believed to have originated the technique. 'Mageblade' was such a specialized disicipline that earned its own distinction.
Witches and warlocks are con-artists who use non-magical means to convince others of magical power. Most practice some form of devil or demon worship to lend credit to their claims.
Occasionally an actual mage will identify as a witch/warlock to hide its true capabilities, in areas where the population will fall for that sort of thing.
Typically, those who make claims of witchcraft are shunned and looked down upon by actual magic users, and the term itself is often met with hostility. In other words, call yourself a 'witch' and someone will probably spit on you.