Haunted Houses are meant to do 2 things in my view: 1) Scare you. After all, it's in the name. HAUNTED House, HAUNTED maze, HAUNTED walkthrough, etc. Sure, it could have a hospital, oceanic, or even an amusement park theme, but it's core purpose is to scare the guest. And 2) Have a more 'realistic' and personal experience. In most haunts, it's people and some theming scaring people, not just theming. In dark rides, the ride has the same program presented to all guests, regardless of age, maturity, fear tolerance, etc. In a haunt, the actors could 'target' those who seem more scared/get a better reaction. For the realism bit, again, it's people scaring people, not a giant monster or robot. The set is also usually a realistic one- an abandoned ranch house, a graveyard, a hospital, etc. In dark rides, you have more unrealistic things happening in a (sometimes) unrealistic environment.
Dark rides are just more of a sensory-based experience. For example, in JLBFM, you have moving vehicles, fog, fire, and other effects that makes your senses 'activate'(not sure how to word that bit). Also, the purpose usually isn't to scare you. Sure, there might be a few jump scares throughout the ride, but they aren't meant to be defining factors of the ride. They're meant to make you seem as if you're in the world of that theme. Examples, in JLBFM, you're trying to help save the Justice League by going through the city to find them. In Spiderman, you're going through Manhattan, being attacked by numerous Supervillains as Spiderman tries to fend them off. Even in something simple like Gobbler Getaway, you go back in time to the first Thanksgiving to try and get all the turkeys back. Also, some dark rides have an interactive feature, which most of the time is shooting targets. In haunted houses, you just walk through them. In these, you shoot at the set/screen to try and progress the story/ride. Even in plain dark rides where you just sit and look at the set, refer to what I said before- it's the same program with all riders. Even if the ride was meant to scare you, there's no chance it can scare every person riding it. Everyone has different levels of tolerance when it comes to scary things.
Tldr; haunts are designed to scare you on a realistic/personal level. Dark rides are meant to trigger your senses and make you immersed in the world the dark ride takes place in.