The Grey Order is an order of wizards who support the lesser known gods such as Armadyl or the Desert pantheon, or were not religious. They were one of the founding orders of the first Wizards' Tower.
Although Grey Wizards weren't responsible for creating many spells, they were known as critical thinkers and were responsible for contributing to pure magical theory.
In the Rune Memories quest dialogue, when questioning Wizard Ellaron in the lobby of the Wizards' Tower, he states that "She [Ariane] is a Grey Wizard: clever but naive." He also mentions her being a Grey wizard in his diary, found in the Red Order study during the quest.