Terror is an extreme emotion invoked by fear. Horror, on the other hand, reminds most of movies or scary tales. It's a genre of media. "Terrifying" directly describes something that causes terror and fear while "Horrifying" describes something that is supposed to be scary. In short, terror and fear are hand in hand, but horror is more related to being scared, which can be caused by a mere sudden movement rather than a legitimate fear/phobia.
There's something about that word which just grips the hearts of many. When you're in a moment of outright terror, that's the word to describe it. Horror is just an adjective to describe terror, so it's not really that hardcore of a word. But terror is a real thing. It's something that causes fear.
I feel that the word horrifying is far more scary to most people than the word terrifying. Perhaps the reason is because our culture has used the term "horror" more readily, especially in terms of genre for such things as movies and books. Because we have such a close association to this word, established by popular culture, it immediately draws images to mind in a way that "terrifying" does not.