Now, the horror vs. UF discussion I think could last a while. I tend to think of horror as being considerably darker than UF, but there is some pretty dark UF out there, so... Your mileage may vary.
I've heard it this way, and it makes sense to me:
Dark Fantasy: horrible things happen, but the protag perserveres and there's at least hope at the end. --Even if people die, they won something with their lives, and things are better in that fictional world because of what the protags accomplished.
Stephen King wrote both kinds, to me: The Stand was dark fantasy--horrible things happened and people had to pay a heavy price, but those who stood strong got help in the end and people won--they won the right to start fresh and clean.
Horror: horrible things happen, and no matter what the protag does, it's just not quite good enough. --Readers are left with the feeling of sadness or despair, or that the protag, if he lives, will just be fighting a losing battle.
The best horror is that way, to me--Stephen King's Carrie--she tried her best, but her mom's and the town's horribleness broke her will and finally killed her. And not only that, but another girl is born who will go through the same because of her differentness.