I've taken part in a few, and read or heard many more, discussions on this subject. None of them have precisely expressed what I think makes a horror story. So here is my opinion, for what it's worth.
For starters, there is no one definition of horror.
Oh, that's really helpful, isn't it?
Yes, but there's more.
Many people have said that if an author intends to scare the reader, that makes the work Horror. More have said if the material scares the reader, the work is Horror.
If that were the case, The Rise and Fall of the Third Reich
Oh, no, wait, that actually happened, didn't it?
No, horror, as I define it, is a work of fiction. And horrific fiction quite happily divides into three types.
Type One
Works set in our world, as we know it, with few, if any, changes. Examples might be The Silence of the Lambs
Type Two
If Type One is things that do happen, then Type Two is things that could happen, given a few changes. Aliens conquer the world. Crazed military scientist unleashes a Doomsday virus (or it escapes). Neural networks become self-aware. Consider The Puppetmasters
So what does that leave?
Type Three
Things that could never happen. I'm really, really sorry, folks. There are no vampires, werewolves, ghosts, demons, dragons, djinns or zombies. It's a great shame, 'cos I love them too. But they aren't real. Never could be, never will be.
That doesn't stop us writing about them. This, to me, is Horror. Supernatural, playing with death and beyond.
There is a caveat here - the action must take place in a world that is recognisably ours, but with nasties added. For example Bag of Bones
So there you have it - a story about something that could never exist, added into our world, and scaring the crap out of us, because we've suspended belief and accepted that there are vampires and evil deities resurrected from the dawn of time.
Now that's proper Horror.