J.R.R. Tolkien, in On Fairy-Stories, writes:
Supernatural is a dangerous and difficult word in any of its senses, looser or stricter. But to fairies it can hardly be applied, unless super is taken merely as a superlative prefix. For it is man who is, in contrast to the fairies, supernatural (and often of diminutive stature); whereas they are natural, far more natural than he. Such is their doom.
My first (mis)reading of this passage was that fairies are "supernatural" only in an indexical sense: the fairies can say of us that we are "supernatural", since we go beyond their nature, and thus far we can say of them that they are "supernatural". But this reading would have Tolkien allowing that fairies are in some sense "supernatural", and he doesn't seem to want to do that; moreover, this reading can't make sense of "Such is their doom."
I now think that Tolkien's idea is that fairies are tied to nature in a way in which we are not. Their doom is to be spirits associated with the woods and so on, while man has a doom that goes over and beyond nature--a doom to union with or eternal separation from God.
That said, I think one might want to distinguish the absolutely supernatural from the relatively supernatural. The absolutely supernatural is God and that whose concept includes the concept of God, such as union with God. But maybe there is room for an indexical notion of the relatively supernatural: x correctly says that y is supernatural if y has powers that go beyond a mere intensification and/or recombination of the powers of x. In such a case, one could have a world that has both fairies and humans, where the fairies correctly say of the humans that they are supernatural (e.g., because they can engage in intentional tool-making) while the humans correctly say of the fairies that they are supernatural (e.g., because they can directly transmute one object into another).
The distinction between absolutely and relatively supernatural mirrors that between the absolutely and relatively infinite, which I will try to say something about on a later occasion.