The Ainur are the spirits who existed with Ilúvatar, and helped him to create the world Arda through the Music of the Ainur. After the creation of Arda, many of the Ainur worked to guide and order its growth. Of these there were fifteen more powerful than the rest. Fourteen became the Valar. The fifteenth, Melkor, became the first Dark Lord. The lesser Ainur that accompanied the Valar into Arda are known as the Maiar.
The Angels are the spirits who existed with the Creator, and helped him to administer the world through the Creator System. After the creation of Man, many of the Candidates worked to guide and order its growth. Four became the Angels. The Fifth, Morningstar, became the first Shadow Lord. The lesser Angels that accompanied the Angels into battle are known as the Human Angels.
I swear I never read the Simarillion. :)
That and the idea that what Hanna is doing is EXACTLY the job description of a Valkyrie makes you wonder about the global-consciousness-library-myth thing and about where fiction comes from.