After some years/decades of book & paper & pencil & dice role-playing games (RPGs, (Advanced) Dungeons & Dragons (D&D) etc.) 'mage' became popular abbreviation of 'magician/'magic-user': all generic/sex-neutral, derived from Persian-Greek male magician word, magus, and 1980s D&D also (re)constructed (based on same languages) female equivalent maga. Fine to say 'mage', but I think in ancient times (Dark/Mediaeval/Viking, whatever age/era of Asian-type countries (Classical?) in Tribulations of a Magician (ToAM)) if using non-generic noble/royal titles such as 'Lord'/'Emperor' & 'Lady'/'Empress', I argue they'd likely say 'magus' & 'maga' (sometimes preceded by 'Arch'... 'magician' seems more common outside 2000s games... at least more classic fantasy literature). My D&D (1990s) gaming groups moved to newer/abbreviation terms I consider overused, so I went back to 'magician', 'magus'/'wizard' & 'maga'/'witch'.
In some RPGs, fighter-magician characters (ToAM main character (MC) Tomas, etc.) get combined titles: Lord Magus/Wizard (or Lady Maga/Witch)... clearly Tomas is still pretty good fighter, but I guess not focused on it, and if I recall correctly (IIRC) some call him 'Lord', so I'm not saying expand title, but if non-player characters (NPCs) want to be very formal (standard when first meeting important person) perhaps they'd use long titles... often royals' ones are quite long (one was <name> by the Grace of God, of the United Kingdom of Great Britain and Ireland and of the British Dominions beyond the Seas, King, Defender of the Faith, Emperor of India) which might add interesting setting details such if emperor & empress have long titles (or Tomas gets military leadership position).
Whether formal/long titles get used, I'm more interested seeing love interest (LI) ladies with (option for) more vulva hair... less popular after popularity of pornography on Internet, but also fits setting (and more popular among older gamers, still large audience). ToAM is often closer to such old style anyway.
That being said, ToAM is excellent how it is: excellent art/writing... of 25+ science fiction & fantasy (SFF) visual novels/games I played, ToaM (haven't played his SF yet) is in my top #1 favourite category (equalled by only two or three others, including The Sorcerer).
While it is indeed fun to "Play" a role and be very thorough about it's lore as possible, I can't see the relevance of the words origins, evolution or even provenance.
What do I mean? Well, this isn't an historically based game set in a Medieval European society. In fact very few Fantasy stories are. They are fictional and they create a Universe loosely based on a romanticized version of several periods of history. Some are more closely related to Western Europe, others drink from the vastness of Eastern Europe and Western Asia. Some follow the Southern influences of the Middle East, others the Slavic and Scandinavian treasures of lore, myth and religions.
Your taking of a narrow view of the role of Mage, in this story is DOA for that reason. In this case, as in several others, it is the World Builder that defines the role and the titles, loosely based in some tradition, surely, but not exclusively.
As genre, High Fantasy, whether in book form or in a visual medium like this one, can't and should NEVER be tied down by excessively narrow definitions and rules about Lore. It is way, way, way, better to let each world builder free to include, transform, adapt, invent, create and use whatever lore and rules they found a connection with.
If you haven't noticed, both here and in The Sorcerer, Talothral incorporates oriental people, black people, whites of all colors, in the stories. This could never, would never, be possible in that narrow view of Fantasy in a British Medieval setting.
So, let's just read and enjoy the world building Talothral makes for us, without tying none of it to what words meant when or where. If you can't understand the role, because the Title means something to you that doesn't fit into what the creator meant, ask. It's not that hard to figure out that a Mage, is someone that uses Magic, whatever that may be.
I'll let you go, but, please don't face Fantasy as something that has to be strict and needs to follow arbitrary rules and roles. Letting it be free and able to go in flights of fancy is it's strongest and most appealing quality.
Peace
