[Infornific]

For Ritual Magic, I'd go with calling it Witchcraft and practitioners Witches (and maybe Warlocks.) That should keep it distinct from your old school GURPS Magic wizards. So that suggests your magic users break out as follows:

Arcane Magic Users

All: Referred to as Mages or Magicians

Wizardry: Based on standard GURPS Magic, spells as skills.

Witchcraft: Ritual Path/Book Magic

Possibly adding in Sorcery using the new GURPS Powers supplement? I'm not clear whether or not you want to do that.

Divine Magic Users

All: Theurgists (esoteric, but I'm trying to come up with something generic and separate from specific type.)

Formally trained, in the hierarchy: Clerics sounds right - the word implies formal rules and scholarship. It's not clear what you use here - Power Investiture? If you're fond of the Rolemaster terminology you could also call it Channeling.

Gifted: I liked the suggestion of Thaumaturge. Mystic might work as well. I would assume Divine Favor or simply Powers. People might be uneasy with these magic users - saints tend to live short lives and end in messy deaths.