These terms can be used interchangeably. They all mean magic practitioner, though each is of different origins, and has meaning based on the language and the people it originates from.
wizard
early 15c.,
wisard, "philosopher, sage, person possessing great wisdom," often with a suggestion of use for evil ends; from Middle English
wys "wise"
witch
Middle English
wicche, from Old English
wicce "female magician, sorceress," in later use especially "a woman supposed to have dealings with the devil or evil spirits and to be able by their cooperation to perform supernatural acts," fem. of Old English
wicca "sorcerer, wizard, man who practices witchcraft or magic," from verb
wiccian "to practice witchcraft."
sorcerer
early 15c., "conjurer of spirits, one who uses magic arts in divination," an extended form of earlier sorcer (late 14c.), which is from Old French sorcier, from Medieval Latin sortarius "teller of fortunes by lot; sorcerer" (also source of Spanish sortero, Italian sortiere; see sorcery).
mage
"magician, enchanter," c. 1400, Englished form of Latin magus "magician, learned magician," from Greek magos, a word used for the Persian learned and priestly class as portrayed in the Bible (said by ancient historians to have been originally the name of a Median tribe), from Old Persian magush "magician"
warlock
Middle English war-lou, from Old English warloga "traitor, liar, enemy, devil," from war "faith, fidelity; a compact, agreement, covenant," from Proto-Germanic *wera- (source also of Old High German wara "truth," Old Norse varar "solemn promise, vow"). This is reconstructed to be from PIE root *were-o- "true, trustworthy."
The second element is an agent noun related to leogan "to lie" (see lie (v.1)). Compare Old English wordloga "deceiver, liar").
The original primary sense seems to have been "oath-breaker;" it was given special application to the devil (c. 1000), but also used of giants and cannibals. The meaning "one in league with the devil" is recorded from c. 1300.
The ending in -ck (1680s) and the specific meaning "male equivalent of a witch" (1560s) are from Scottish. Related: Warlockery.
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So in the end... use what you relate to the best.
I use Mage for myself.