As is often the case, talking epistemology with John Shuck combines with my own reading in mythopoetics, fantasy and theology and results in me dealing with a few terms that I find helpful to use consistently.
In each case, I'll use a brief description, followed by a list of what is generally valued in each mode of expression. Lastly, I'll throw up a few examples that come to mind.
In the comment thread conversation I had with John Shuck most recently, I called myths "structures of meaning that tell us the truth about ourselves and the world and invite us to live into that truth more fully." This isn't a bad definition, and I'll go with it for now. Myths can also be described as "stories that make stories". A myth is primordial because it gives rise to many other stories of other kinds. It is powerful because it guides people as they make stories of their own lives and experiences, as well as those of their community. A myth becomes a myth, in part, due to it's broad use. A myth that gives rise to no stories is no myth. It is much easier to recognize older myths because we can see whether they have stood the test of time.
Values: evocative power, invitation, broad applicability, iterative richness, "meaning", valuation, generative power (stories that make stories)
Examples: the Bible as a whole and many of it's parts individually, the Bhagavad Gita, the Mahabharata, the cycle of trickster stories of Coyote and Raven and Spider etc., the Koran, the Prose and Poetic Eddas, the Ennuma Elish
Myth is the purview of religion and spirituality.
A Fairy Tale
Tolkien gives the best definition of what he calls "fairy stories" in his essay and lecture "On Fairy Stories". It is a relatively long lecture, actually, and he has a lot to say, but in brief, he defines a fairy story as providing four benefits: fantasy, escape, consolation and recovery.
He is using fantasy in the medieval sense, that is, in using the mind's faculties to imagine things that do not or cannot exist. One example he uses is "green sun". For escape, Tolkien is reclaiming escapism as something good; 'the escape from a prison rather than the flight of the deserter'. Consolation doesn't need much explanation - a good fairy story provides consolation in the midst of life that is often unsatisfactory in some way. Lastly, Tolkien talks about recovery - that is, recovery of wonder at everyday things, or recovery of vividness of experience. He gives examples like "tree" or "fire" or "bread and wine", things that he feels he understands better thanks for fairy stories than he would have without them.
Fairy stories help us to see our world differently. The basic structure of a fairy story is an introduction to the familiar, a journey into the other, unfamiliar world, and a return to the familiar, having been changed by what was experienced in the unfamiliar world.
Values: fantasy, escape, consolation, recovery, otherworldliness, the familiar-made-strange and the strange-made-familiar
Examples: The Hobbit, Avatar, The Eternal Sunshine of the Spotless Mind,
A fairy story is a particular kind of story that is close to myth.
A series of events purposefully organized by an author or authors for a purpose other than description. It's actually pretty challenging to define a story, but for my purposes, I think the above will work. A story has to have a storyteller, either an individual or a community; it has to be intentionally arranged from start to finish, and it can't just be a bare recounting of events, because that falls into the last category that I'm looking at. A big difference one can see is between what makes a "good" story and what makes a "good" description.
Values: expressive craft, narrative beauty, coherence, characterization, drama, irony, evocative imagery
Examples: Beowulf, Anansi Boys, The A-Team, The Great Gatsby, Pride and Prejudice, Harry Potter and the Sorcerer's Stone
Story is the purview of authors and storytellers.
A series of events organized logically and chronologically. The assumption is that something has occurred, and has been observed, and then the description attempts to express those observations to someone who was not present.
Values: technical accuracy, functionalism, reductionism, efficiency of expression, clarity
Examples: the physical origins of the universe, a blueprint, an instruction manual, a technical schematic, a genogram
Description is the purview of science.
What's open is to discuss which of these we are dealing with at any given time. What is not an option is pretending they are all the same thing.