Cryomancer
Arcane
Generalist wizards are wizards capable of learning any type of spell in game with no restriction. Specialized Wizards are those only capable of casting a portion of the spells.
Among retroclones, Lamentations of the Flame Princess is the most iconic example of Generalist Casters. Astonishing Swordsmen & Sorcerers of Hyperborea is the most iconic example of Specialized Wizards. A Cryomancer can't cast fireball for example, a Pyromancer can. Cryomancers also can't cast invisibility, illusionists can.
Some games are "hybrid". Gothic 3 for eg, you can learn most basic spells regardless of a path. But powerful high level spells like Hailstorm,and Time bubble(Water), Army of Darkness(Dark) and Meteor(Fire) being locked till you side with a deity and his "agenda". Gothic 2 locks you as a Fire mage and you can't become a necromancer under Xardas apprenticeship nor a Water Mage under Saturas apprenticeship. However, the game allows fire mages to learn how to cast high level dark magic like Army of Darkness in Innos monastery(don't ask me how Pyrokar is OK with it) which makes spell casters in G2 "generalist". The mod Returning 2.0 "breaks" the magic, and you as a necromancer, guru or water mage, can't learn how to cast powerful fire spells like Fire Rain. Each faction has unique spell lists.
Some games allow both. You can play Baldur's Gate 1/2 as a specialized caster or as a generalist caster.
Among retroclones, Lamentations of the Flame Princess is the most iconic example of Generalist Casters. Astonishing Swordsmen & Sorcerers of Hyperborea is the most iconic example of Specialized Wizards. A Cryomancer can't cast fireball for example, a Pyromancer can. Cryomancers also can't cast invisibility, illusionists can.
Some games are "hybrid". Gothic 3 for eg, you can learn most basic spells regardless of a path. But powerful high level spells like Hailstorm,and Time bubble(Water), Army of Darkness(Dark) and Meteor(Fire) being locked till you side with a deity and his "agenda". Gothic 2 locks you as a Fire mage and you can't become a necromancer under Xardas apprenticeship nor a Water Mage under Saturas apprenticeship. However, the game allows fire mages to learn how to cast high level dark magic like Army of Darkness in Innos monastery(don't ask me how Pyrokar is OK with it) which makes spell casters in G2 "generalist". The mod Returning 2.0 "breaks" the magic, and you as a necromancer, guru or water mage, can't learn how to cast powerful fire spells like Fire Rain. Each faction has unique spell lists.
Some games allow both. You can play Baldur's Gate 1/2 as a specialized caster or as a generalist caster.