Ruling States with influence that contain a Council of Mages, who, in their right, reign over their owned territories, are known simply as Magocracies. A typical Magocracy doesn't necessarily own a lot of territory, and most are commonly found on islands. However, Magocracies are officially recognized as independent nations by other neighboring nations, and as such conduct their own rules in their given territories. While Magocracies may be ruled by mages, they are not exclusively inhabited by mage citizens. Many non-mage citizens inhabit Magocracies as well.
The same goes for Mage City States. While ruled by mages, the majority of citizens will be of non-magical affiliations. What typically determines a Magocracy and Mage City State is the presence of a Mage Academy or any other major institutions of magical learning. While Mage Schools can be found in a large number of non-mage ruled cities, Academies can only be found within the influence of a mage-ruled city or state. Academies are more official, better financed and larger institutions of magical learning and mage-training.
Most initiates of these Mage Academies will most likely come from rich families, as the tuition can be quite steep under the guarantee that students will become fully trained mages upon graduation.