In my mind, I see the major difference in the motivation of the author, as well as the theme of the story.
In a horror, the idea is to set someone up for fear and terror, for terror's sake. Redemption usually consists of survival of the protagonist. Whether you take Fredie or Jason, mostly the idea is everyone is at risk of dying. Happily, the protagonist makes it out alive.
In a Dark Fantasy (My Opinion), you have a higher objective. The goal is someone setting out to save/redeem/ create something lasting. With Lord of the Rings, you have countless "Moral of the story". You have faithfulness, loyalty, love.
In a Jason movie, you may have people banding together, but in general, that is simply the only way to survive. Whereas with Frodo, you have someone who could have lived a fairly simply life without problems if he just said, "No, it's not my problem" And he multiple chances to lay down this burden.
However, deep in the back of his mind is his love for the shire, and the realization that if he doesn't do this, the world he loves and people he cares about, suffer.
The story I'm trying to finish up now fits in this Genre. It was never intended to be dark, but in my mind, life is sometimes like a dark fantasy. In a sense, you can get involved in noble pursuits that become very ugly, and you have the same dilema Frodo has, you face the beast, or you say, "Not my problem."
I can't say my goal was ever to freak people out in the least. Rather, it was and is (not simply to entertain), but to make people think.
However, you really can't accomplish that objective without making the case that something monumental is on the line.
You have to make some kind of case that "evil" is "evil", and not benign. And it can be a metaphorical evil, but if you look at many evils, as Tolkien did, they are sometimes a product of some twisted concept of doing good.
Now, I'm not making his case, but one point is, "If you sacrifice paradise for an easier life (machines), have you really improved life?"
I love stuff that makes you think. To borrow from John Lennon, "I love to turn you on..." But not in an acid or other pleasure sense, in the sense of introducing a novel thought, like planting a seed.