Is The Witcher low or high fantasy?
The other two current answers I’ve seen for this question have confused terms. “Low fantasy” is a distinct subgenre from urban fantasy, which is what they seem to be talking about. The distinction from high fantasy isn’t the setting so much as the stakes.
High fantasy, or epic fantasy, is patterned along the lines of The Lord of the Rings. The scale is epic, mythic: a world other than our own, evil incarnate, the deaths of nations, the kinds of things you might have seen in an ancient mythology—Tolkien’s Legendarium was conceptualized as a “modern mythology”. One key distinction from heroic fantasy is that the great evil is typically not defeated by the hero challenging the villain through force of arms, but through nonviolent means, because violence really only makes the Big Bad Evil Guy stronger.
In The Lord of the Rings, the One Ring represents evil itself, the motive to bind the world under tyranny. It could never be destroyed by a heroic prince on a white horse—that’s Boromir, and Aragorn—or by a great wizard who can shatter cities with a word—that’s Gandalf. Instead, the Ring ultimately destroys itself given the opportunity, through the hold it has over Smeagol, by the sheer dumb luck of three farm boys from the Shire (counting Smeagol) who never wanted to be caught up in this whole mess in the first place. Tolkien himself disliked the then-common comparison of his work to World War II, commenting that if he’d intended to base it on the war, he would have written the Fellowship using the Ring against Sauron as a weapon.
In the original Star Wars trilogy—fundamentally a high fantasy story, albeit told with the toolset of space opera—Luke Skywalker ultimately defeats the evil Emperor not with his magic (the Force) or his sword (lightsaber), but by refusing to strike him down in anger and thereby setting an example that convinces his fallen failure of a father to do the right thing for the right reasons for probably the first time in his entire life. Anakin sacrifices himself to destroy Palpatine for love of his son, winning freedom for the galaxy as a byproduct.
The Deed of Paksenarrion by Elizabeth Moon starts out looking like low fantasy and transitions to become high fantasy by the end of the trilogy. Paks, as a paladin, defeats the evil cult of Liart not with the sword, but by surrendering to them and simply refusing to be broken by days of torture.
High fantasy is often confused with heroic fantasy. This is a little more down-to-earth, more classic pulp adventure fiction. Archetypically, some chosen knight on a white horse with a cadre of quirky companions defeats the BBEG in combat and gets to marry the beautiful princess. As I alluded, if it had been Aragorn, the heir of Gondor returned, who defeated Sauron with his magic sword, that would have been heroic fantasy. The Jedi Knights, Anakin, Yoda, and Obi-wan included, all thought they were the heroes of a heroic fantasy setting when they really weren’t: the Emperor was simply too powerful to kill with a lightsaber the way the Sith Lords of old had been defeated.
Unlike the original trilogy, Knights of the Old Republic on the light-side path really is a heroic fantasy story: Revan has a gang of funny friends, and even the badder guys like Canderous Ordo and HK-47 are more lovable anti-heroes than evil. And in the end Revan slays Darth Malak and gets the girl (in Legends, Revan is canonically male and had a family with Bastila Shan before disappearing to do battle with the Sith Emperor).
The core rules of Dungeons & Dragons are pretty much written with heroic fantasy in mind, and the tropes are so well known in Japanese RPGs like Dragon Quest and the early Final Fantasy games that these days parodies and deconstructions like Goblin Slayer and Maoyu: Archenemy and Hero are almost as common over there as the genuine article.
Low fantasy is still typically set in a basically medieval, pre-gunpowder world, it often even has Tolkien-style elves and dwarves and the like, but it’s meant to look more like the real world in terms of how people act. There’s often plenty of magic and politics, but what there typically isn’t is world-saving heroics: the genre often deconstructs those as tending to cause more problems than they solve. It’s more friendly to anti-heroic protagonists and even the antagonists often have shades of gray to them.
And finally we reach The Witcher. Geralt is no hero; in fact he pretty much pooh-poohs the concept. He’s an outcast vagabond who kills monsters for a living—and as he once puts it, the steel blade is not for humans and the silver blade is not for monsters, they’re both for monsters, and he’s as willing to take your coin to slay the two-legged kind as not. But trying to “save the world” beyond that just isn’t his thing: he realized after his first outing that it tends to cause more problems than it solves. He’s content to make his money and have a good roll in the hay with willing women when he can find them. And he really never deals with any kind of world-threatening danger: it's all nations fighting other nations for normal human reasons, but with elves, dwarves, and critters from Eastern European folklore involved.
For another example, Steelflower by Lilith Saintcrow. Kaia Steelflower is no heroine. She’s a sellsword, thief, and sometimes assassin whose big dream is to just open a tavern. At one point she interacts with somebody who does think he’s in a heroic fantasy story, an old contact who is now leading an army against a purported evil king based on a prophecy, and basically thinks she’s the girl he’s going to get. She’s having none of that nonsense and she and her companions leave him after a couple battles to pursue their own interests.
A Song of Ice and Fire is a low fantasy world bordering on dark fantasy. It’s much more concerned with the damaging effects of mortal politics on people than with the coming end of the world. Knights aren’t particularly heroic (with some notable exceptions like Ser Barristan), the beautiful queen is a toxic narcissist who’s schtupping her twin brother behind the King’s back, the “only” honorable nobleman is so anal-retentive about his honor it gets him beheaded as a traitor, his son is undone by the fact he can’t keep his pants zipped, et cetera. The whole thing is meant as a metaphor for how real-world humanity is being undone by its own character flaws: we’re so busy fighting with each other for petty power we can’t work together to effectively tackle truly global problems (the Others, White Walkers in the show, specifically represent anthropogenic climate change).
The light novel series Goblin Slayer is a low fantasy plot in a heroic fantasy setting. There’s frequent mentions of a “hero party” doing battle with the Demon Lord (a new one apparently arises in a recurring cycle every couple of decades), but the story instead focuses on an adventurer who specializes in slaying goblins. Goblins are treated as a starter enemy by most adventurers, but can still do significant damage when left unchecked while the higher-level adventurers are off battling the Demon Lord.
Get even less optimistic and you get dark fantasy. Like high fantasy and heroic fantasy, there is true evil in the world, not just people pettily screwing with each other. Unlike high fantasy and heroic fantasy, it’s winning. The world just generally sucks: the best you can hope for out of anybody, even the protagonists, is moral ambiguity. And it often has a lot in common with horror fiction.
Berserk by Kentaro Miura is dark fantasy. Innocents die in horrible ways, nations are destroyed by eldritch horrors, and Guts, the protagonist, is a wandering swordsman who endlessly slays horrific demons without having much hope of ever achieving any kind of final victory. And it was all set off by the betrayal of the man he considered his best friend: Griffith, a charming sociopath dreaming of a kingdom of his own, and has gained that kingdom as a demonic god, Femto.
Warhammer 40,000 is dark fantasy IN SPACE! The legions of mankind, orders of knights and warrior priestesses and billions upon billions of ordinary human soldiers, ruled by an emperor on life support and an uncaring, incompetent bureaucracy, have been locked for thousands of years in endless warfare against aliens, otherworldly horrors, and frequently each other. And they’re losing.
“To be a man in such times is to be one amongst untold billions. It is to live in the cruelest and most bloody regime imaginable. These are the tales of those times. Forget the power of technology and science, for so much has been forgotten, never to be re-learned. Forget the promise of progress and understanding, for in the grim dark future there is only war. There is no peace amongst the stars, only an eternity of carnage and slaughter, and the laughter of thirsting gods.” — Vulkan, Primarch of the XVIII Legiones Astartes "Salamanders"
Drew Karpyshyn’s Darth Bane trilogy is Star Wars as dark fantasy. The story has a duo of outright villain protagonists, namely Bane and his apprentice Darth Zannah, who work in the shadows to destroy the weak and failing Brotherhood of Darkness to establish a new Sith order that will ultimately produce Emperor Sheev “Darth Sidious” Palpatine a thousand years from now. And they are horrible people.
So that’s the four basic categories of fantasy fiction in terms of scale and people. There’s other varieties in terms of setting, however.
Urban fantasy is a distinction of setting more than stakes and scale. Rather than set in a classic fantasy setting (e.g. a world patterned after medieval Europe), it’s set in literally our present-day real world but with fantasy added in. It tends to lend itself more to low fantasy or dark fantasy in terms of characterization, though. Think vampires, werewolves, and wizards living in the shadows of New York City, Chicago, or Hong Kong, usually unbeknownst to regular people.
The Dresden Files by Jim Butcher: wizard for hire fights supernatural baddies in Chicago
Dark Heavens by Kylie Chan: Aussie woman falls in love with Hong Kong businessman who turns out to be an ancient Chinese god
Deadly Curiosities by Gail Z. Martin: Charleston, SC antiques dealer banishes angry ghosts on the side
Bone Street Rumba by Daniel Jose Older: half-dead Afro-Caribbean man polices the ghosts of the fully dead in NYC
Historical fantasy takes place in our real Earth, but is set in our historical past.
Queen of Zazzau by J.S. Emuakpor takes place in 16th century Nigeria, based on the mythology surrounding the semi-legendary Hausa warrior-queen Amina who ruled a small empire there in the time period. Born a princess of the city-state of Zazzau, after her lover is murdered by a rival king during a parley gone wrong, she makes a pact with the god of war, becoming his bride (and submissive) in exchange for the power to take the fight to her enemies.
Kushiel’s Legacy by Jacqueline Carey is a sort of magical alternate history where things took an odd turn after the Crucifixion of Christ: rather than the Resurrection, Jesus’s blood spilled on the ground birthed a part-divine, part-earthly being called Elua, who walked the earth and called angels to follow him. They eventually founded a nation in the real-world location of France, Terre d’Ange, under the precept “love as thou wilt”, which is where the protagonists of the first two trilogies are from (the third is a descendant of a d’Angeline but born and raised in Alba, i.e. Celtic Britain).
The first trilogy is basically high fantasy, starring a sacred prostitute who eventually quests to learn and then speak the name of God to banish a fallen angel and break an ancient curse.
The second is more heroic fantasy, with the protagonist being a prince who goes through tribulations in foreign lands to save his true love and his nation.