Top "fun" or interesting but not haunting horror movies:
Alien
The Thing
Friday The 13th Part 6
Evil Dead 2
House (1985)
(A lot of runner ups in the fun category, including basically all of the Jeffery Combs catalog, but I'm not even sure those can be considered "horror" instead of comedy with horror trappings. Similar to Dead Heat and the like.)
The Shining is certainly a flavor of horror. I think part of the problem of trying to make a list where the only criteria is horror sweeps up such a broad array of movies. Like Hostel, From Beyond, Alien, and Silence of the Lambs are all equally in the same bucket, which doesn't seem right.
There are a lot of way to sort the distinctions, but The Shining is deserving of a slot somewhere in the realm of supernatural horror. It relies on creepy atmosphere and a descent into isolation with audience along with the characters, more than blood splattering, or some kind existential question to shake the audience. It is, at its core, a haunted house movie.
Invasion of the body snatcher is the movie i watched when i was like 8 at a friends house. After that i had to walk home by myself at night. I never ran that fast home and never felt that scared, in kind of a good way. I never felt like that again and i'm not super into horror movies anyway, but that must be what junkies talk about when they say they chase that first "high" except for horror movies. A few years ago i discovered the band wolfie's just fine, and their song reminded me a lot of that experience.
https://youtu.be/qG8iAtpavK4?si=7bIu109xXBdY68aG
I caught the original b&w version when I was about the same age, spent a month checking under the bed for pods. I feel you!
I think it's a generational thing too... there have been so many versions of that story it can hit everyone:
The original was 1956. Then the remake in 1978. "Body Snatchers" in 1993 which is creepy as hell, and apparently "The Invasion" in 2007 which I somehow missed.
The Wicker Man is at the very top for me, I never seek out horror films as any sort of fan of the genre, and this one transcends it.
So does Evil Dead 2. As well as The Shining.
So that's three. Alien also belongs up there. Four down, one to go...
I'll round it out with The Exorcist. And you know why that film was so shocking for the time? Because it wasn't filmed as a horror film, but as a family drama. That dry context is what made it feel so immediate for seventies audiences, and it's still effective today, as it's not a conceit nor gimmick, it's an artistic statement of intent.