This staff was created under a single guiding principle--by wizards, for wizards.
This weapon's Japanese name is pronounced the same as the Wizard's Staff. 魔導師 (madōshi?) is a Japanese word that refers to a user of magic, however in the Final Fantasy series the mages are usually referred to as 魔道士 (madōshi?), which is intentionally pronounced the same but uses different kanji.
The two weapons technically mean the same thing, so the inclusion of "High" in this weapon's name product of the localization to distinguish it and reflect that it is stronger than the other similarly named staff.
Staff that holds powerful magic.
High Mage Staff is the second strongest weapon for Vivi, providing 32 Attack, inflicts Silence when attacking with it while equipped with Add Status, and teaches the abilities Meteor and Osmose. It can be found from Chocograph 13 (Forbidden Forest) or bought for 6,000 gil at Black Mage Village during endgame.
Vivi has the High Mage's Staff as a weapon for his Bring Arts figure.