Tolkien's subcreation - his Legendarium as a whole - is often described as a modern "myth" or its mythic qualities are emphasized. I do not think this is correct, because of a quality of myth that seems essential, but is distinct from the situation with Tolkien's work.
I will first describe what I regard as an essential attribute of a myth - which is that a myth is distinct from any specific expression, and particular "version", of that myth...
While, on the other side; Tolkien's world is ultimately rooted in his own work: his own rather specific words and the actual published structure.
"Fuzziness" - imprecision - seems to be a characteristic of a myth; such that the specific form in which a myth is expressed - e.g. its exact words - does not seem to matter very much. It is as if the myth has a life of its down, and the words or images by which a myth is presented are not its origin; but serve some secondary purpose, as reminders or pointers.
The two great myths of England are King Arthur - including Merlin; and Robin Hood and his Merry Men.
When I think of either of these, no specific version comes to mind; and indeed I find that none of the versions of these myths is very satisfactory.
For instance, whenever I decide to read one of the Arthur accounts - whether historical (Geoffrey of Monmouth, Layamon, Malory) or a modern description, novel, story, TV programme or movie - I am often overwhelmed with a kind of irritation at their inadequacy; and end-up quitting, bailing-out before I have gone very far.
The best I can hope for is odd and brief hints, images, phrases, or gestures; that imply rather than depict the mythical - and many versions lack even this.
I also find the "explanations" of myth to be unsatisfactory - and when a myth gets decoded or unpacked, and its supposed underlying meaning is described - this too always distorts the "reality", and again often evokes a rather strong sense of rejection, or even revulsion.
So what is the myth? On the one hand it is nebulous, indefinable; on the other hand the particular feeling and expectation that it evokes is quite precise.
If I am engaging with some version of Arthur I seem to have a pretty clear grasp of what I am looking for and what is valid - even if I could not say just what that is.
But really, the situation with respect to myth is not really unusual. After all - much the same applies to such everyday and real-life matters as our attitude to a place or nations, or loving a particular someone.
A real myth is a kind of "miniature" or "model" of something in real life. The situation is just that any specific "model" we make of reality, is really just that: a model; whether it is made of words, pictures, or theories.
A model is made by leaving-out almost everything, and only including a few things - so it never captures real life, always distorts it; and indeed the relationship between the model and the real is itself indefinable. And the number of ways that any actual model is wrong are innumerably large.
Unless we have some way of knowing reality directly, and without intermediary communications such as words, images, stories, or other models; then we cannot ever know it At All.
At bottom, our ability genuinely to live in a relationship with this world depends on the ability to know directly and unmediated; and we need to decide, each for himself, whether or not this direct knowing is actually real and actually happens.
By this account a myth that "works" and is not a fail or fake, works first for one person at a time - no matter how national (or international) it may supposedly be; and secondly by a direct, person-to-person sharing of that myth.
And this situation is the bottom line "collective" mythic reality, towards which any particular version of a myth may gesture - or not.
From the above, if the argument is regarded as valid; it seems that Tolkien's world is not a myth-proper; but a literary creation.
The essential depth and relevance of Tolkien's work is not, therefore, the same as that of a myth-proper - although of course there are similarities and overlaps, "mythic qualities" in Tolkien.
This not-myth nature of Tolkien strikes me as significant, because there are malign tendencies that want instead to declare Tolkien's work a myth, with the implication that new "versions" - in other media than literature, and by other authors than Tolkien - validly add-to, re-shape, and re-interpret that myth...
And even, potentially, that these "re-imagined" versions may be equally valid expressions of the "Tolkien myth".
In a nutshell; when Tolkien's world is regarded as a myth, then Tolkien himself and his published work are nothing more than the first and oldest expression of a universal and universally-accessible myth. This line or reasoning would justify - indeed already has "justified" - an "open-season" of commercialization, exploitations, subversions, and inversions of Tolkien's work.