I was intrigued about the question, so I surfed around and came up with the following notions:
The villains control the plot: they create obstacles/problems that the protagonists must overcome against the clock and while overcoming a personal difficulty/problem. There are usually high stakes.
It's not necessarily clear where the obstacles/problems come from, that is, it isn't clear who the villain is. The villains may even be the protagonists themselves.
It produces a sense of excitement or, more to the point, it produces a 'thrill'. There is hope it will end well for the protagonist while there is anxiety/fear about whether they will fail or, more likely, what they'll have to sacrifice to be successful.
In the end, the 'good' will likely win and, if it doesn't, the fiction will bring about a sense of being too close to the general concept of reality's unsatisfying justice.
The important thing is that, by the end, reason and logic pervail in keeping society stable and well-structured. People know the rules and know that breaking them will bring about consequences. If the villains manage to escape those consequences, the fiction becomes closer to reality, but the rules of the society and the world are not endangered.
It produces a sense of fear. There may be hope it will end well for the protagonist, but it's less certain whether it will.
If it ends well, there will be this sense of the world having been shaken but it's still possible to come back to normalcy, or a semblance of it. If it ends badly, there will be this sense that the world is shattered and there's no going back to normalcy.
The important thing is that, by the end, reason and logic do not pervail in keeping society stable and well-structured. The rules have been overthrown. Even if they are once more imposed (eg. the villain is punished), it is clearly as a mask to hide the terrifying and unpreditable unknown (eg. a new villain - or the same - may pop up again at any time).
There's a general atmosphere of threat, but a recognisable one. This can include death or life-threatening events, but not necessarily so.
There's a general atmosphere of menace, but usually an unrecognisable one.
Both require techniques to build up tension and suspense, as well as plot twists. The difference is in the intensity of responses ellicited.
Furthermore, it is important to keep in mind there are two main types of horror, one of supernatural origin (also known as dark or Gothic fantasy to avoid prejudice associated with the term 'horror') and one of non-supernatural origin (also known as psychological thriller to avoid prejudice associated with the term 'horror')
In reference to H.P. Lovecraft, there is no greater fear than the fear of the unknown so, in the end, one could say that the seminal difference between thriller and horror is that one ellicits fear of known threats while the other ellicits fear of unknown threats.
The tools to create the fear (and the excitement one derives from it) are fundamentally the same; whereas the theme and effect are different.