Fantasy: stories about power and how it’s found, lost, and used.
In Low fantasy, characters have no struggles with power (Conan the Barbarian) they are always confident of their powers (like superheroes) and rarely question themselves or their powers. Sword & Sorcery. Their struggles are against more powerful beings, not themselves or their own weaknesses. Frodo, being half the height of a man, and thus a much less powerful being than the Men or Elves he hangs around with, gains ultimate power over Sauron. Though the necessity of Gollum there in the Cracks of Doom, is an ironic flourish.
Horror is a subgenre of Fantasy. Thus it also is concerned with power. But the most prevalent theme in horror is fear. What scares us, to some extent is also what renders us powerless. Acrophobia, is the fear of giving into a sudden and overpowering impulse to jump making us doubt our power over our own actions. Claustrophobia, is fear of being in a tight, confined space, where the power to move is greatly incapacitated, making us doubt our ability to function to breathe on a physiological level.
The New American Gothic (S. King, Danse Macabre) is a story in which the character's morbid introspection drives the plot. Rooted in narcissism and anxiety (the self-centered fear of Alcoholics Anonymous), the new American Gothic concerns the inability to see beyond the horizon of the self. This closed minded, compartmentalized, blinkered, bracketed cognition on the part of the protagonist is the impetus for horror. Constantin Stanislavski's "Circles of Attention" reduced to a fierce, laser like dot of light in the center of the self. These characters have axes to grind, fierce prejudices to overcome, preconceived notions to abandon, malevolent childhoods to rise above, addictions to accept.
Also, the New American Gothic protagonist is different from the noir protagonist because their fears are existential rather than actual. The perfect example of a New American Gothic protagonist is Jack Torrance from The Shining.