Horror fiction, horror literature and also horror fantasy is a genre of literature, which is intended to, or has the capacity to frighten its readers, scare or startle viewers/readers by inducing feelings of horror and terror. It creates an eerie and frightening atmosphere. Horror can be either supernatural or non-supernatural. Often the central menace of a work of Horror fiction can be interpreted as a metaphor for the larger fears of a society. The genre has ancient origins which were reformulated in the 18th century as Gothic horror, with publication of the Castle of Otranto (1764) by Horace Walpole.
Horror fiction has its roots in folklore and religious traditions, focusing on death, the afterlife, evil, the demonic and the principle of the thing embodied in the person. These were manifested in stories of witches, vampires, werewolves, ghosts, and demonic pacts such as that of Faust.
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Supernatural Fiction is fiction involving the supernatural, as in magical beings and forces outside of the laws of our physical universe. The supernaturalism in this case is based more off of medieval Catholicism than modern, atheistic, naturalistic philosophies. That's not to say all these stories fit in with biblical canon but if you do the research you'll find a cultural, evolutionary link with many medieval myths and superstitions. This evolutionary link is helped by giving Gothic Fiction honorary membership into supernatural fiction.
While dealing with the same subject matter supernatural fiction sets itself apart from Horror and Thrillers with supernatural elements by focusing less on the scream and thrill factors and more on the supernatural elements. In the past Fantasy was restricted to the Standard Fantasy Setting but the rise of Urban Fantasy and Dark Fantasy is making the distinction between fantasy and supernatural fiction very dubious. Alternatively people might put urban fantasy and related genres under the label supernatural fantasy and put fantasies based off the standard fantasy setting under the label epic fantasy. Supernatural Fiction doesn't have to show how fantastical elements are affected by modern society like urban fantasy has to.
Weird West and Supernatural Soap Opera are subgenres. Usually marketed as Horror, Thriller, or Fantasy (with an emphasis on the words paranormal and supernatural). Sometimes marketed as Science Fiction.