How can you tell a story between a thriller and a horror? To me, horror are like thrillers except they have supernatural entities to add scary conflict among the characters. And thrillers deal with suspense and fear without the supernatural. I thought most stories that have psychopathic killers are usually in thriller stories, but people dubbed them to be horror. If a story is about a killer, how can it be a horror story if it doesn't have any supernatural elements? And isn't both of these genres are about fear and suspense?
Horror doesn't imply supernatural entities. While they are similar genres, to me the difference is that the primary emotion in a horror novel should be fear, while in a thriller it should be excitement. Both deal with tension and suspense and certainly both can have both fear and excitement, but it's a matter of which is more prevalent (imo; you could look up an official description of the two but I'm sure the specifics even differs from publisher to publisher, which is debatably what counts the most). I also tend to think of thrillers as having 'happy' endings whereas horror needn't, necessarily.
Where are you getting the idea that either horror or thriller implies supernatural? A thriller is meant to thrill a horror is meant to horrify. It's like PG and PG-13. Thrillers tend to be more action centralized. Lot of suspense and mystery. Horrors tend to be darker.