I don't doubt you but I haven't heard all these terms used in the way you have used them. I have heard "epic" fantasy used for what you call high fantasy. I agree though in order to converse you have to define the terms. These boards can get very frustrating fast otherwise.You are all confusing high fantasy with high magic. High fantasy has the characters deeply rooted to be HEROES. Some of them might die but they do it epically and gloriously. They aren't nameless smucks traveling around doing random quests.
This is an example of terminology meaning different things to different people. I also consider LOTR Low fantasy. Specifically, I see it as low-middle Fantasy. Things like Harry Potter are High Fantasy. To me has to do with how much it it is weighted down by reality and how much supernatural elements like magic is in it.
5e seems to make room for both. I think. *crosses fingers*
Holy thread necro, Batman! I think the evidence is clear that levels 1 and 2 are definitely "apprentice" levels, and things can get pretty dicey for PC's (very analogous to 3E in numbers). Starting at level 3 yields 4E style power-level and hit-points, so hopefully all parties should be satisfied with the result.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.