I think you're misinterpreting the quote on the wiki. Since the creation of this question, the wiki quote has actually changed, however.
All tier spells in YGGDRASIL could be categorized into four great systems of magic, each one with some exclusive spells and characteristics. Not only that, but magic casters too are also categorized by the system of magic that they use. (emphasis yours)
I believe this simply means that tier magic is categorized into 4 systems of magic: Arcane, Divine, Spiritual, and Alternative. In the same way, magic casters are categorized by the 4 systems of magic. Arcane Magic Caster, Divine Magic Caster, Spiritual Magic Caster, and Alternative Magic Caster.
Arcane Type Magic Caster: Elementalist, Sorcerer, etc.
Divine Type Magic Caster: Cleric, Hierophant, etc.
Spiritual Type Magic Caster: Talisman User, Shaman, etc.
There are other categories like Blessing type, that belong to the Alternative system:
Blessing Type Magic Caster: Bard, Paladin, Cursed Knight, etc.
Runecraft and Wild Magic are completely different forms of magic from Tier Magic. Magic casters in the New World are practitioners of Tier Magic.
All tier spells in YGGDRASIL could be categorized into four great systems of magic. (emphasis mine)
Runecraft and Wild Magic were forms of magic that were created LONG before the introduction of Tier Magic. These forms of magic were limited to specific races, and are now very rare in the New World.