Thriller is a whole other genre from horror. The Interpretor is classified as a thriller, but you wouldn't classify it as horror. Lucky Number Slevin is classified as thriller and it even has extreme violence, blood, and body count, but you wouldn't call it horror.

The Sixth Sense stands on the line between horror and thriller. It can get subcategorized as suspense thriller to give a better idea of what it is doing.

I see the horror genre as having to do with primarily fear. If the point of the movie (or let's rather say what the filmmaker's intention) is to (attempt to) scare you, then the movie is horror. Scream, while it has a lot of suspense and thriller elements, is primarily horror because it wanted to evoke fear in its viewers.

Back to the Sixth Sense, the goal there was to intrigue you and even curdle that pit of your stomach, but not to scare you. Mystery movies are suspense because they are not looking to scare you, but they have a lot of the elements that make up a horror movie. The Sixth Sense has a lot of these elements as well.

Of course, this can be debated until we're dead, but those are my opinions.

I once heard that horror is fear and terror is finding out. I don't know if that's technically true, but it stuck with me.  

Films from the horror genre are designed to elicit fright, fear, terror, disgust or horror from viewers. In horror film plots, evil forces, events, or characters, sometimes of supernatural origin, intrude into the everyday world. Horror film characters include vampires, zombies , monsters, serial killers, and a range of other fear-inspiring characters. Early horror films often drew inspiration from characters and stories from classic literature, such as Dracula, Frankenstein, The Mummy, The Wolf Man, The Phantom of the Opera and Dr. Jekyll and Mr. Hyde.

http://en.wikipedia.org/wiki/Horror_film

Terror" can refer to a genre that may overlap with horror or horror fiction.

http://en.wikipedia.org/wiki/Genre

http://en.wikipedia.org/wiki/Horror_fiction

I've always thought that horror was the genre itself and terror was one of its elements. I've even seen a few movies in which terror was actually contained in the MPAA rating description. Terror, to me, implies suspense while horror can imply many things.

ter·ror     
–noun 1. intense, sharp, overmastering fear: to be frantic with terror.  
2. an instance or cause of intense fear or anxiety; quality of causing terror: to be a terror to evildoers.  
3. any period of frightful violence or bloodshed likened to the Reign of Terror in France.  
4. violence or threats of violence used for intimidation or coercion; terrorism.  
5. Informal. a person or thing that is especially annoying or unpleasant.  



hor·ror
–noun 1. an overwhelming and painful feeling caused by something frightfully shocking, terrifying, or revolting; a shuddering fear: to shrink back from a mutilated corpse in horror.  
2. anything that causes such a feeling: killing, looting, and other horrors of war.  
3. such a feeling as a quality or condition: to have known the horror of slow starvation.  
4. a strong aversion; abhorrence: to have a horror of emotional outbursts.  
5. Informal. something considered bad or tasteless: That wallpaper is a horror. The party was a horror.  



Close enough to be synonyms.