I feel like throwing my two cents in. To define "High Fantasy", I'd like to first define "Fantasy". The main purpose is to allow us a story about a place that is not here, with its own history, people, and geography that isn't necessarily congruent with our own. From there, we have our dial. The lower the dial, the more a Fantasy world will reflect our own. At the lowest, it is merely a place and events that are not real, everything within it is otherwise how we understand our own world to work. The more we turn the dial, the more strange, magical, and otherwise alien it becomes. High fantasy has towns with potion shops, hedge wizards learning spells from a book at the local library, and monsters out in the wilds as populous as the squirrels and birds. Strange is normal.
TL;DR: Fantasy is shit that didn't happen, High Fantasy is shit that didn't happen and everyone is a wizard riding a mechanical dragon.