High Fantasy for me is about the feel of the setting (wondrous), not the power level of the characters.
High Fantasy - Tolkien, Donaldson (Thomas Covenant), Le Guin (Earthsea), Cheryh (Chronicles of Morgaine), CS Lewis (Narnia)
Low Fantasy (sword & sorcery) - Conan, Leiber (Lankhmar), Thieves' World, Wolfe (Book of the New Sun).
Moorcock (Corum, Elric, Hawkmoon) does a sort of high fantasy sword & sorcery, in feel though he's closer to Leiber than to Tolkien or Donaldson.
Generally, High Fantasy has clear-cut good & evil and a hierarchical universe where the champions of good strive to maintain the status quo vs the forces of Change & Entropy - it favours Law, in D&D alignment terms. The strongest influence on high fantasy is Judaeo-Christian morality and dualist mythologies (eg Norse, Persian). Examples go back a long way, most tellings of Arthurian myth fit here.
Low fantasy tends to have fuzzy good & evil, and the protagonists are often agents of Change - it is Chaotic, in D&D alignment terms. Its universe is often democratic and individualist. It seems to be largely of 20th century post-WW1 origin. The strongest influencies would seem to be Enlightenment, Rationalist (or nihilist) and atheist philosophies, and pagan non-dualist mythologies (eg Greek).
Standard D&D and its derivatives (eg Diablo CRPG) mix the genres and is better classed as 'power fantasy' than either high or low.