The Fantasy subgenres: some thoughts

• Arguably the first s&s story was written by Robert E. Howard (creator of Conan). "The Shadow Kingdom" was published in Weird Tales in 1929.
• The phrase "Sword & Sorcery" was coined by Fritz Leiber in 1961
• Joe McCullough argues that what sets apart a s&s story from other fantasy are three qualities of the main character: self-motivated, outsiders, of heroic stature.
• I'd quibble with Joe's nomenclature a bit, but by and large agree. S&S protagonists by and large choose adventure, rather than have it thrust on them. They do not, by and large, have a defined, accepted and acceptable place in the cultures of their milleux, (barbarian, thief, what have you). And if by 'heroic stature' Joe means they have some skill or ability that makes them extraordinary, then I agree to that one for the most part as well.
• But. Always a but. There are exceptions. There are always exceptions. Jirel of Joiry could not be considered an outsider, despite being a female feudal lord in an ersatz medieval France, as her vassals accept her rule without question. Few would argue that Jack Vance's Dying Earth stories, especially Cugel's Saga, were not Sword & Sorcery, though the setting is technically a future Earth rather than an alternate one. But Cugel is a character that refuses to be pigeon-holed. He is self-motivated in the sense that Joe means; Cugel has absolutely no interest in subscribing to the mores of whatever society he finds himself in, unless subscribing offers him some material benefit. Cugel is definitely an outsider, no matter where he finds himself. But Cugel's only extraordinary ability, or rather abilities, are 1. an inability to learn from his mistakes or alter his behavior to minimize conflict, and 2. a sheer, stupid, bloody-minded tenacity.
• Sword & Sorcery is not High Fantasy, though it can be Epic Fantasy or the more recent 'Gritty Fantasy' (or as I prefer to call it, 'Low Fantasy' but not as an aspersion, just to highlight the fact that it is consciously tying to counter some specific conventions of High Fantasy) . 
• I would break it down this way: In all these categories, the 'fate of the world' may (or is it 'might') be at stake; but in High Fantasy, generally speaking it must be at stake as a genre convention. Or so the subgenre have evolved. High Fantasy, a la Lord of the Rings. 'Nuff said.
• Low Fantasy can mix and match from any of the other genres, except when it comes to tone. The tone is generally more akin to Chandler than Tolkien. This is fantasy with the voice of a meat packer rather than an Oxford don. This is fantasy a la Joe Abercrombie. There are no Tom Bombadils traipsing around, singing songs. There is, however, torture, rape, and unflinching delving into the not nice parts of being human. Look at The Heroes. It's a big bastard of a book about, what, a three day battle that nobody essentially wins and is pretty much a pointless waste of lives. It's good stuff, seriously, but it can't help but be what it is: an allergic reaction to High Fantasy. 
• Epic Fantasy, I would argue, tends to straddle a midpoint between high and low. Martin's A Song of Ice and Fire and Jordan's Wheel of Time are the most celebrated examples of the subgenre, though they are very different series. Martin writes very little in the way of magic. It's there, but it's a tiny portion of the whole, and frankly much less important than other themes; themes he tends to share with the Low Fantasy genre. The fate of the world isn't really in question, rather the fate of individuals, families, and ultimately nations. There are no prophesies; every character has agency or not according to their own personality. The Wheel of Time by contrast is absolutely stuffed with magic and the fate of the world does hang in the balance in every book. Prophecies abound. Characters struggle fruitlessly to escape their destinies.
• So why isn't Martin's Song Low Fantasy? And why isn't Jordan's Wheel High Fantasy? Because I say so. 
• No, it's because Martin writes primarily to illuminate rather than to shock. Also because Song has more DNA from Shakespeare's historical plays than it does from Tolkien or Smith et. al. It wasn't written as a response to the perceived weaknesses or failings of High Fantasy, even subconsciously. So it is free to roam the very wide bounds of the Epic subgenre.
• Jordan, despite his dyed in the wool High Fantasy tropes, still wrote with the same sort of vitality he honed when writing the Conan books (yes, he wrote Conan Sword & Sorcery books long after Howard died.) He build a towering edifice of High Fantasy, but he built it on a Sword & Sorcery foundation. Matrim Cauthon could not exist in a Tolkien novel. In the end, High Fantasy has a very specific formula, and that formula calls for certain ingredients and forbids others. Just because you have a farmboy fulfilling a prophesy and a Dark Lord bent on utter domination, that doesn't automatically get you into the club.
• And what about my lovely Sword & Sorcery? What are its hallmarks? Beyond the protagonist's requirements, there's blessed brevity. S&S is a natural fit for short stories, not series. If there is a series, it's the characters, not the plot, that continue on through multiple books. The focus tends to be on action more than character development, though this doesn not mean that characters are cardboard. Generally speaking the writing is much, much tighter.

Insomnia, I have made you at least mildly useful.