As mentioned the tone, but also the win condition. In fantasy the goal is to go on an adventure, experience a world full of wonder and defeat the evil entity. In dark fantasy the goal is to survive in a world full of wonder and perils, the antagonists you face aren't always much worse than you.

In horror on the other hand the win condition is surviving at all, and you're more likely to die horribly. Defeating the enemy is not really on the menu.