Haunted Mansion, to me, largely DOESN'T have a story. At least not as designed. It's been watered down in recent years to at least have some sort of story, but as originally imagined, it's just an eclectic mix of ghouls with no overarching story. Sometimes, we see stories that aren't really there due to that awful Eddie Murphy movie, too.
What is Pirates' story now? I can't figure it out. The forced Captain Jack story confuses me and I hate that every fourth phrase is "Captain Jack Sparrow" which no one calls him in the films. It would have been fun to incorporate that gag, actually.