Black Magician is magigian that can use Black Magic.
Sachakans generally do not make this distinction as The use of Black/Higher magic is common.
The Guild of Kyralia created an official position with this name for such magicians after the Ichani Invasion. They are classed as a Guild Higher Magician, but have rules attached to the position. Black Magicians cannot leave the city of Imardin without the agreement of the High Lord and/or Administrator, they may also not teach others except for Black Magic to those appointed by the Guild, or in special circumstances
|Spoilers from "The High Lord"|
Technically, Akkarin is one of the Guild's Black Magicians, however the position was created after his learning and usage of Black Magic during the Ichani Invasion. Sonea becomes the first to be put in the new position, and the rules are set so she may help the poor people of the city.
|Spoilers from "The Ambassador's Mission"|
Kallen has also been appointed Black Magician so that he may watch Sonea just in case she flouts the rules, so that the Guild have someone on par with her abilities. Sonea does the same for Kallen.
|Spoilers from "The Rogue"|