What is the difference between "horrify" and "terrify"?

When would I use one, versus using the other?

According to the online dictionary (thefreedictionary.com), they can be used as synonyms, but it leads one to believe that horrify would be more related with something [intensely] shocking, whereas terrify would be more related with fright or intense fear.

Something that would horrify you would definitely scare you, but probably more along the lines of being overly grotesque — think of films like "Halloween", "Nightmare on Elm Street", "Friday the 13th", "Saw", etc. They scare you, but make use of a lot of gore (blood, body parts being removed, etc.); thus, the "horror" film category.

I would say something along the lines of "6th Sense" or "Signs" would be terrifying; not really a lot of gore, but the thought of coming face to face with a ghost or an alien would most likely scare you [fill you with terror] to the point where you couldn't move.

To add to Will's answer, I think there is an element of shock and surprise in 'horrify' which there isn't in 'terrify'.

I could quite easily continue to be terrified by something that terrified me yesterday, whereas I think that if I was horrified by something yesterday, today I'm more likely just disgusted.

As an interesting aside, note that horrify:horrific <> terrify:terrific.

Horror is something that, on an elemental level, makes you feel absolute revulsion and rejection. I am horrified when I read about mothers who murdered their infants by microwaving them. My gut just clenches and turns on itself with the thought of what that child went through before it died.

Terror is something that invokes an instinctual 'fight or flight' response - someone sneaking up behind you and scaring you, the sensation of centipedes running over your skin - it makes your heart race and your adrenaline rush.

Even though Mary Shelley's monster terrorized both its creator, Dr Frankenstein, and the surrounding village, it is in the genre of Gothic horror. I think this is because the reader is horrified at Dr. Frankenstein's obsession with working with dead bodies and creating life from death.

This work makes you feel horror (revulsion) rather than terror (fear).

My professor of Shakespeare taught that terror makes you flee (people will run away from a terrorist bombing) while horror draws you in (people are transfixed by horror movies and deadly car wrecks). Terror = run; horror = stop and stare.