In her excellent Rhetorics of Fantasy, Farah Mendlesohn identifies four major forms of fantasy literature, by looking at the way in which the fantastic enters into the story, which might be roughly characterized in the following way, using Mendlesohn's labels:
(1) Portal-Quest: The characters enter by some means into a fantastic world.
(2) Immersive: The story occurs in a fantastic world treated as the real world.
(3) Intrusion: The fantastic enters into and disrupts the real world as something foreign to it.
(4) Liminal: The fantastic enters into the real world as if it were part of the real world.
I think we can generalize this a bit, and a notation would be handy in doing so. So let's take a standard set-up, the contrast between the mundane and the fantastic:
There are a few things that need to be recognized about this distinction. It will be important for later that the contrast between the mundane and the fantastic is relative, not absolute; the mundane is the 'rest state' or 'reference point' in the narrative. 'Mundane' here is not a synonym for 'real' and something obviously real can be fantastic relative to someone else. (And both are common parts of human experience. If you fall asleep and dream and then wake-up, you've from mundane to fantastic to mundane again. If you walk through a dark wood and get creeped out, you're in a fantastic state relative to your usual state.) Despite its possibly counterintuitive sound, the fantastic is also the more fundamental of the two notions -- nothing in a narrative is recognizable as mundane except in contrast to the fantastic, but the fantastic in a narrative is fantastic directly to the hearer or reader. While it's tempting to talk about 'the mundane world' and 'the fantastic world', in many situations we are not talking about worlds, but just states or contexts.
The notation we have so far doesn't of itself constitute any sort of story at all; it's just the contrast between the mundane and the fantastic. To get a story we have to do something to that contrast. There are several things we can do.
A mundane element can move into a fantastic context.
A fantastic element can move into a mundane context.
A context recognizable as mundane can turn out also to be fantastic.
A context recognizable as fantastic can be treated as mundane.
These correspond to Mendlesohn's four major kinds of fantasy (portal-quest, intrusion, liminal, and immersive, respectively). However, again, I want to understand these at a more general level; this is not an empirical classification, but a kind of narrative movement. To these four, I think we need to add a fifth:
It can be deliberately ambiguous whether we are dealing with the mundane or fantastic. (This is often how writers try to handle Christmas stories in movies and television shows -- everything is mundane and not fantastic, but there's that one strange thing, so that maybe you were dealing with the fantastic all along? That department store Santa couldn't have really been Santa Claus -- and yet....)
We can call these five 'the standard fantasy structures'. It's important to note that these are structures, not genres or subgenres, although you could define genres of fantasy in terms of them. Because the distinction between the mundane and the fantastic is a relative one, these structures can be nested. You can have a perfectly good story that has a simple fantasy structure. But you can also have more complicated structures, and some of the great works are partly so interesting precisely because of their more complicated structures. For instance, The Lion, the Witch, and the Wardrobe is a paradigmatic example of a portal-quest fantasy, so its pivotal structure is naturally M|>F. The Pevensies enter Narnia. But this is not a complete characterization of the fantasy structure of the work. For one thing, Lucy enters the wardrobe, M|>F, but she returns and seems to her brothers and sister to going crazy. So Lucy's entering the wardrobe and return arguably means that she is the fantastic intruding on the mundane state of her siblings, M>|(M|>F). They end up all going through the wardrobe despite avoiding the wardrobe room because the Macready is leading a tour of the house and she somehow seems to be everywhere until the children have no choice except to enter the wardrobe; the mundane world turns out to be (maybe) fantastic already, although it's not clear, M?(M|>|(M|>F)). In Narnia they meet up with the Beavers and start getting used to the place. But a fantastic thing has happened: Aslan has returned. Narnia has become the reference point; Aslan is fantastic relative to it and is intruding into it, M?(M|>|(M|>F))|F. This is actually extraordinarily important for the character of the story: we've entered a fantastic world and a more fantastic thing is entering into that world. But this is not the end of it. Because of Edmund's betrayal, Aslan has to save him in a way that complies with the Deep Magic from the Dawn of Time, which is a fantastic element discovered in Narnia-as-mundane, (M?(M|>|(M|>F))|F)F|. But, of course, there is a Deeper Magic from Before the Dawn of Time, ((M?(M|>|(M|>F))|F)F|)F|. The Pevensies, however, become Kings and Queens, and later return through the wardrobe again, yet changed, a fantastic element entering the mundane: M<|(((M?(M|>|(M|>F))|F)F|)F|).
Likewise, the pivotal structure of The Lord of the Rings is the fantastic as mundane, since Middle Earth is a contained context and we never enter or leave it: |FM. But the full structure is immensely more complicated, since, for instance, Rohan is mundane compared to Gondor and the Shire is mundane compared to both. Nor is this interaction between mundane and fantastic built in a straightforward fashion of increasing fantastic; the mundane hobbits find the fantastic Riders intruding, and they flee and the story steps up to fantastic Tom Bombadil, and then steps back down to comparatively mundane Elves. This is why quests have become a cliche in fantasy; Tolkien's very sophisticated use of quest structure to take us naturally and easily through a dizzying array of different fantasy structures has led to others trying to replicate the richness of that experience, sometimes using Tolkien's own techniques and sometimes just doing cargo cult imitations.
However, while fantasy structures can nest, this is not the only way they can be related. For instance, the first meeting with Mr Tumnus in LWW is set up simultaneously as mundane Lucy entering fantastic Narnia and as fantastic Daughter of Eve entering mundane Narnia, and done so extraordinarily well. This is done in a way even more central to the story in Prince Caspian: the mundane Pevensies entering fantastic Narnia again are also the fantastic legendary Kings and Queens entering mundane Narnia. Is it primarily a M|>F Pevensie tale or a M<|F Caspian tale? These are not nested structures, furthering a plot in an orderly way, but two structures being used to build the overall story, each treated alternately, and in some passages more or less simultaneously, as if it is the structure of the story. Likewise, while fantasy structures essential to plot tend to nest, unless they are badly done, fantasy structures that are a matter of episode will tend to float relatively free. Lucy having tea with Mr Tumnus is a structured as a |FM that does not, in itself, constitute a plot-building structure but a character-building one; it does not need to connect up with another fantasy structure because the book is not an account of the adventures of a Faun. It's just there so that Mr Tumnus matters and the stage is set for a later crisis.
One sees the distinction very well in cases where a fantastic structure basically floats free in a context that is deliberately eschewing anything fantastic. Dream and hallucination sequences are standard ways in which you get fantasy structures in works that are not part of the fantasy genre by any stretch of the imagination, and you could very well have a story that has nothing fantastic except a dream or a hallucination.
There can also be a great deal of ambiguity about whether a given fantasy structure is of a particular kind or is even in play. For instance, above I suggested that when Lucy returns from Narnia the first time, she comes back as a fantastic intrusion. One could dispute this, I think, although I think some of the structure of the story (in particular, how the Professor handles the matter) requires it. When Edmund goes and returns, that's pretty clearly M|>F for Edmund, but it's not shifting the reader or the other characters about at all; it's not a part of the nested structure of the plot, but just a stage-setting and character-building structure. But one could perhaps say that Lucy's return (although not her going) should be treated the same way, and not, as I've depicted, as an important element of the nested structures constituting the plot. This kind of dispute is unavoidable, I think; people will sometimes just read a story differently. This is not to say that such disputes are irresolvable, of course -- it's a very a great error to assume that the inevitability of dispute implies the irresolvability of dispute. For instance, it's inevitable that people will catch different moral tones in reading a work, and therefore disagree; but people who read The Lord of the Rings as a simplistic tale of Good vs. Evil are provably reading it badly -- you can point to a large quantity of evidence in the story that shows that they are not getting the moral tones right. Likewise, there will inevitably be disputes about how the mundane and the fantastic interact in any very sophisticated story; but there is evidence from which to argue. However, the evidence cannot be assumed in every case to decide every dispute, and if that's the case, we are left with an ambiguity. A general rule, though, is that anything that could happen naturally with regard to a story is something that could be used deliberately by a storyteller, so there may well be cases in which the ambiguity is entirely deliberate and an essential part of the story.