As I see it Academy Mages are undergraduate students and arena mages are professionals.
Isn't academy supposed to be their graduation fight? After the fight, the academy mage is considered a full fledged mage. (age 22-26) An academy mage is still an extremely powerfull person even if weak compared to arena mages. I think they can be considered as a "professional".
Arena mages however are
the best of the best mages that fight in an Arena, in many cases to resolve conflicts between different regions. These guys have been in many battles and have improved through experience and not training. Most professionals never even reaching this power throughout an entire lifetime.
(When reading the stories on the website, it's clear that forces like the necromancer in darkfenne or the rise of the bloodwave warlord isn't something that happens every 2 years. These are not simply professionals)
Speaking of which where are the graduate student mages?
I would consider Naiya and other familiars to be the undergraduate "students" or simply undergraduate mage-like creatures that never reached the level for graduation due to lack of talent/work. Basic knowledge of spells but no stamina or all-round skills.
