Because I am god's own special idiot*, I am ignoring my own advice on fantasy's genres and jotting down my thoughts on what the difference between Epic Fantasy and High Fantasy should be considered as, and why the differentiation matters.
To me it boils down kind of like this. Epic Fantasy is like the Iliad. High Fantasy is like Malory.
Epic Fantasy should be seen as stories that try to tell everything (for given values of everything) about a momentous event. The momentous event can be as big as the fate of the world or as small as one particular land, city or fort - such as Troy. But there's (almost) always an event and it's almost always seen from multiple angles.
High Fantasy should be seen as stories about a person colliding with the supernatural and undergoing trials that challenges them as a person, hopefully for the better. The person (or people) don't have to be entirely free of the supernatural to begin with; they can be a knight with inhuman powers, or a hobbit, or an apprentice wizard. But what they confront will be beyond their ken.
These two definitions are not mutually exclusive and many works fall under both. But nor are they mutually inclusive and there's some sharp differences. Epic Fantasy is set up to be plot-focused; High Fantasy to be character-focused (although neither has to be). Epic Fantasy benefits from PoVs from both sides of the conflict, and arguably should have them to qualify; High Fantasy's task is arguably easier for not showing us the mindset of the mysterious and supernatural beings the protagonist meets. Epic Fantasy requires characters who are suitable close spectators of and participants in these events; High Fantasy requires characters with a certain degree of ignorance, making it highly suited for bildungsromans. And so on. There's probably some points I'm not thinking of.
My point though, I trust, is made. To have a work that is both requires either some canny work in terms of reconciling the differences, or a big canvas. The canniest route is for books to start as High Fantasy and become Epic Fantasy and that is the template of most of the blockbuster books in Trad Fantasy, which admittedly has made it feel less canny due to familiarity.
Where I think I'll get some disagreement is the idea that works that don't have PoVs from both sides of the conflict aren't truly Epic Fantasies, particularly as that disqualifies Lord of the Rings. Is it conceivable to suggest Lord of the Rings is the work that inspired Epic Fantasy by having most of its qualities, yet wasn't actually of the type itself? I think so, although it will fail the common sense sniff test for most.
Certainly though, having both sides shown has become a big part of the genre, and I think to its advantage. It is easy to demonise the other in a war (and Epic Fantasy is usually the tale of a war); it doesn't happen so easily when you see inside their head. And in a way, the idea that Epic is usually the tale of a war further gently pushes me further towards the idea that LotR isn't truly an Epic, for LotR is the tale of a quest, and the war one of the byproducts. War is just a crucible for the character's growth, rather than the source of the story. Perhaps another good example of the difference is that in Epic Fantasy, victory comes about through good old fashioned military domination; in High Fantasy, it is the by-product of the character's growth.
That perhaps accounts for the link between High Fantasy and a moral impulse but dark apotheosis or morality free growth are possible, and have been seen. It's just a far harder sell. Epic Fantasy makes it easier to explore dubious characters.
In this schema, LotR is definitely High and debatably Epic, and is certainly more High than Epic. Likewise, the Fionavar Tapestry. Also High is A Wizard of Earthsea, the Deverry Cycle, The Wounded Kingdoms, much of Pratchett's Witches series, Harry Potter and so on.
In the Epic corner we find Feist's works, Gemmell's Legend, most of Lackey's Heralds of Valdemar, Dominions of the Fallen, American Gods (just about), Tigana, The Deep, Interesting Times, The Traitor Son Cycle and so on.
However, I think the most interesting thing about the link between the two comes from looking at Wheel of Time and A Song of Ice and Fire.
WoT starts off as High Fantasy to its roots. It becomes an Epic around book 3/4, but doesn't abandon the High Fantasy arcs it has set up for its more characters. When we get final victory, while there is a military victory (made possible by Mat's fulfilment of his trials), it mostly comes from Rand's personal victory in understanding and accepting without hate the supernatural fate put on him. It is both Epic and High in a way very few other series are (to me, it is the true start of Epic).
SoIaF however is an Epic from the get go. It doesn't ease the reader in at all. However, once it has set up its nature as an Epic, it gives many of its characters very High Fantasy plotlines. Jon's arc is straight up High as it gets. Dany's arc is very reminiscent of it too, although twisted and inverted in many places. Bran too has many an echo of it, although one somewhat butchered in the meaning of his final trials in the TV series. And so on. Ultimately, it is just as much Epic and High as WoT. It's not a surprise that these are the 800lb gorillas of trad fantasy. Nor is it a surprise that they've gigantic out of control narratives that have nearly undermined what they do.
The point here though is that a book doesn't have to be consistently High or Epic all the way through, and adopting the conceits of the other at particular points for particular purposes is a crowd pleaser. Which is probably why the two genres are so closely linked (well, that and LotR). But they are - or at least should be considered as - two different things with two very different purposes.
But that is my truth, tell me yours.
*as most have noticed, God's Own Special Idiot is a rank claimed by many in these times; there are armies near untold of us. I personally am God's Own Special Idiot number 2521566978, Idiot First Class of the Windmill Tilters, motto "Too smart to be happy and too stupid to be successful"