Different combinations of elements create different mages. For example, Eyrian is a Maelstrom Mage because he weilds elements associated with storms – water, wind, and lightning.
Someone that weilds fire and earth could be called a Vulcan or Vulcanic Mage.
To be an Umbral Mage, one must have affinity for darkness plus at least one “base” element.
To be an Astral Mage, one must have affinity for light plus at least one “base” element.
Crystal and Aether, while considered elements by the scholars of Avrirsa, are not something that can be wielded like the other elements.
Crystal is the physical manifestation of Aether, and can be utilized in jewelry or other Magitech devices. Usually it has an elemental affinity…but it is possible to find unaspected crystals in the world.
Aether is like the lifeforce of Avrirsa. It isn’t something you can observe with the naked eye but it is what gives crystals their elemental affinity. It’s what affects the people and creatures of Avrirsa, shaping what their abilities as a mage are.
Scholars have speculated that the Elder Gods may be capable of wielding aether since They created it.