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(This is better now that it's been edited...) It may sound odd, but I think the main criterion is how the story treats death. If death is one possible threat among many (being captured, being tor...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/10562 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/10562 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
(This is better now that it's been edited...) It may sound odd, but I think the main criterion is how the story treats _death._ If death is one possible threat among many (being captured, being tortured, the macguffin falling to the enemy, blackmail, heartbreak, public exposure, humiliation, political scandal, strategic losses, military losses, code being broken, plague being released), I'd call it a thriller. If death or near-fatal injury is the main threat (nurse threatening to chop off feet, having to cut off your hand to get out of a bear trap, running through the woods to get away from chainsaw-wielding maniac, serial killer, rabid dog trying to break into car, psychotic supernatural clown drowning you in sewer), I'd call it horror.