As mostly explained before,
Alchemists are metallurgists and brewers (in the thought of tinctures not alcohol)
A witch is a practitioner of natural magicks.
Magi are literally translated as "Wise Men"
Wizards are ones who develop ability in magic from study, while...
Sorcerers and Sorceresses are born with them naturally.
Enchanters and Enchantresses typically rely on guile and emotional manipulation (to my knowledge)
Warlocks are the typically darker, more sinister figures. Oath Breakers.
Some others you may find neat:
Sages and Mystics are very similar to magi, but with more spiritual than magical focus.
Seers, Oracles, Prophets, Psychics, etc. are knowers of the future. Fortune tellers. Diviners. Some through intentional divination, others through prophetic dreams (I fall in that one), and some through external influence.
Shamans are spiritually connected people, often of a more tribal nature due to the unfortunate decline in Shamanism. They commune with the Otherside, the Good Neighbors, etc. Whatever there is to communicate with on a supernatural level.
(Terra/Pyro/Cryo/Necro/Vita/Aero)-mancers are manipulators of a specified element (Earth/Fire/Ice/Death or Undeath/Life/and Air respectively)
There are other lesser known ones, but that should cover you for now. If you need a full list and description, email me or ask another question. Never stop believing in magick!