"Fantasy" always implies a secondary world to me. Magic/magical creatures in what is supposed to be our world (i.e., the primary world) falls under "Paranormal/Supernatural [romance, thriller, mystery, etc.]" or "Magical realism" in my book (I admit I might be the only one with said book).
"Low Fantasy" for me is "opposite of what Tolkien did," and since Tolkien had intended to write some kind of epos (like Beowulf), the combination of "magic+chivalric adventure" is what defines High Fantasy for me. I happen to think that the amount of chivalric tropes defines the "level" of fantasy, not necessarily the amount of magic (though the amount of magic must be >0).
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"Low Fantasy" for me is "opposite of what Tolkien did," and since Tolkien had intended to write some kind of epos (like Beowulf), the combination of "magic+chivalric adventure" is what defines High Fantasy for me. I happen to think that the amount of chivalric tropes defines the "level" of fantasy, not necessarily the amount of magic (though the amount of magic must be >0).