So, half brain fart, half can't sleep, but decided to just have the in verse elven language have a few quirks. Mostly in that some combination words translate the same, but have very different meanings. I will of course, be looking at the top five magical rankings, in ascending order.
Fifth place belongs to the Master Wizards, who are not only fully trained and accredited mages, but are as often as not? Administrators and politicians. In fact, Master Wizards who focus on the political side of thing are technically called Magisters (Magistrix being the female title in more common usage) and can vary in actual power and skill. But generally speaking, if someone uses the title Master Wizard, they are solidly competent and trained, but not elites.
Archmages are the next step up... and are usually just politically pointed Master Wizards, and as such? There is a massive gulf in this groups potential skill and power level, because yes, you can technically reach this position with barely any ability to cast magic so long as you have some political sway.
On the other hand, Arch Mages require you to defend your position with extreme violence, because they refuse to let weak little bitches dilute the brand. This is where the fact that elves took over comes into play, as both forms of Arch Mage are made of the same elements... but are used differently. In this case, the element meaning Mage is before the one meaning Lady (because its a reverse sexual morality world after all). Effectively, putting magic before politics. These are the hardcore magical academics.
Then you have High Arch Mages. Now, the ritual that is part of the process has a number of effects, but at the end of the day? A High Arch Mage is effectively Lich Adjacent and are totally not related to the undead in any way, shape or form, despite the many similarities. However, no necromancy (aside from technical soul magic and manipulation) is used on pain of unraveling and death. In many ways, facing a High Arch Mage is facing a highly mobile artillery battery who can alter their ammunition on the fly and has a staggering array of options for wrecking you. You are a strategic threat, but one that can be planned and accounted for.
And lastly, we have the Celestial High Arch Mages. Basically, the closest D&D equivalent to them are the Chosen of Mystra or demigods of magic. When you get to this level, you are forced to deal with politics, because you are a strategic national asset more than capable of crushing armies in the field and razing cities to the ground with minimal, if any, support. Effectively? Celestial High Arch Mage Talindria Tracan is an nine hundred and thirty two year old woman who holds her rank of High Lady by her own merits, entirely separate from her blood. At this level of power, you are capable of setting your own diplomatic status, and the mighty worry about what your buttons are and how to reign you in, as they have to specially include you in their plans, and not just generalized plans, but specific ones.
Effectively, its the 'too powerful to give a fuck what you plebs think' level. Its a fantasy world. Magical power buys a LOT of leeway and exceptions, even if there would be some brain breaking as it can take a long time to climb the ranks.
But essentially, as you climb the ranks, political connections and pull matter less and less outside of where you get your education resources, and the more sheer raw power and skill count.