You have it backwards. Witch is not the same as mage.
A female of the witch variety is a “witch” and the male counterpart is “warlock”
Mage isn’t a gender specific word, but Sorcerer is (M: Sorcerer F: Sorceress)
You lost sight of naming conventions when you tried to call them something else. Every new name you think of has different rules.
Yes, a female mage is basically a witch.
Might explain why the Zandalari call Jaina a witch. 
“She’s from Kul’Tiras and uses magics against us! … Must be one of those hag witches we hear of from de’ continent.”
Also, gnomes are small and thus not very heavy.
Escapes, freeze traps the other three, and runs off screaming with the trinket
“De hideous Kul’tiran Witch woman is back! Throw her with de Blood Trolls mon!”
Magitrix or Enchantress.
Magitrix sounds like a mage versed in telepathic manipulation of whips and other torture toys…
Mage is Mage.
Wizard / Witch would be the gendered terms for a similar concept, I think.
Sorcerer / Sorceress if you really wanted to, but even there Sorcerer isn’t male-specific and so could technically be used for both.
Witch tends to also be associated as the female version of Warlock, but at that point we’re doubling up and it just comes down to which magical terms the setting is using. I get the impression that it (Warlock) is very much a gender neutral term in the Warcraft setting.
Latin is the only way.
Male: Magus
Female: MAGA
wait…
A…Mage…ra. Magera. Me…megera. MEGERA !
ROFL, c’mon OP, everyone knows girls can’t be mages. Well, now, they can summon food. so there is cooking involved. I guess let them be mages too, I guess.
Mage is an androgynous word for “magus” or for people who use magic. They encompass:
Wizard (male)
Sorcerer (male)
Sorceress (female)
Witch (female)
Warlock (male witch)
A witch is more in line with a warlock, yeah. I think mage is unisex.
After careful consideration I’ve come to the conclusion that female mages should be burned at the stake as that is the only fitting end to such abominations.
I would say no… witch entails different schools of magic then the arcane and elements alone. It would be more fitting to call a female shaman or warlock a witch. Mage is to scholarly for such a title.
The other two legit talk to rocks or believe they are getting the better end of faustian bargains. Clearly unenlightened mongrels.