I broadly categorize horror movies into three groups: Slashers, Creepers, and Creatures.
Slashers are the most “in your face” of the bunch; they have the big franchises, like Halloween, Nightmare on Elm Street, and Friday the 13th. They deal with a killer, or on occasion killers, killing people. They rely on repulsion for a lot of their “scare” value, and they feature a lot of blood and gore. They tend to be the cheapest kind of horror to make, usually don’t have a very strong script as a result, and usually reliably make money, so they keep churning 'em out. There are thought-provoking, well-written, and well-made movies in this category, so it shouldn’t be discounted entirely.
Creepers are more strongly scripted than slashers; they use story, rather than graphic visuals, to create fear and dread. Get Out and Hereditary are good recent examples. Sometimes there’s blood and gore, but it’s usually not the focus. They’re harder to make effectively, because they rely on a strong story and a good filmmaker.
Creatures are exactly what they sound like: a horror movie that features some kind of thing. Such as The Thing, come to think of it. The creature can be human-like, like Dracula or Frankenstein, or just weird, like The Blob. There can be lots, like Piranha, or just one, like Jaws.
Of course, there’s a lot of cross-over. Child’s Play is a slasher, but also sort of a creature movie. The Thing is clearly a creature movie, but it has strong slasher-like qualities. The Exorcist fits all three categories to some degree.
And there are also sub-categories. “Torture porn” seems to me to be a subset of slasher that heightens the visuals to an extreme degree and makes pain, rather than fear, the focus. My favorite subset of Creature films is the “Giant Killer Something” movie, where some massive monster is destroying everything. Eight Legged Freaks would be one such movie. Even the Godzilla movies are sort of Giant Killer Something movies.
Thrillers are another thing entirely, not in the family of horror. The way I see it, thrillers are about danger, while horror is about fear.
Edited to add: I should mention that I’m something of an extremeophile when it comes to horror. I have a drawer that I call “my ‘What The Fuck Is WRONG With You?!’ drawer”, because sharing the movies within would probably lose me some friends.