Tolkien uses Eldar and High Elves, with different meanings (the ones me and Cleg explained in previous posts). The term 'High Elves' is not made up by Christopher. It is mentioned in the LotR, for instance when Frodo meets Gildor and his company, as Ngugi said above. Specifically after he hears their song, Frodo says: 'These are High Elves! They spoke the name of Elbereth!' (Elbereth is the name the High Elves used for Varda.)
'High Elves' is not used in different contexts, and it has only one meaning, which is: the Calaquendi, the "Elves of Light", those of the Eldar who lived in Aman and saw the Light of the Trees, as opposed to those who didn't, the Moriquendi (also called the Úmanyar, those of the Eldar who were "not of Aman", as the name says [opposite: Amanyar]).
Edit: Funny how people can argue so much about something fictional.