'Power at Great Wizard Level' and 'True Great Wizard' are not the same.
The latter is the backbone of the Mage Alliance. Each Great Wizard has a seat in the Alliance's highest authority, the Great Wizard Conference, where they can participate in votes, discuss alliance policies, and decide the fate of ordinary wizards and even the course of time. Each of their names is well-known in the alliance.
The former merely possesses some traits of Great Wizards—such as a massive true form, formidable magic power, or extreme mastery of certain types of magic, etc.—capable of demonstrating battle abilities equivalent to Great Wizard level in a short period, making them 'Registered Wizards', fundamentally different from true Great Wizards.
However, because they have touched the boundary between top registered wizards and Great Wizards or even reached over with a few fingers, many wizards privately call these individuals 'Quasi-Great Wizards' or 'Pseudo-Great Wizards'.
