I think that yes, it depends. As a general approach I would suggest your sound should reflect the message being conveyed, which can include any and all of the things you mentioned. However, personally I wouldn’t set any hard and fast rules about these things as I don’t think any one solution can be considered the correct one. There are so many variables it’s more a case of what you think is right for your project - setting rules would not allow for experimentation or creativity.
For example there may be a scene where there is tension between two characters - it’s likely the sound will follow that narrative and look to garner an appropriate emotional response from the audience. This situation entails both what the character is feeling and what story is telling and it’s really down to how you want to approach it. You could design sound from a very internal, perceptual standpoint of one particular character where they gradually become more scared or angry over the course of the scene or you could take a more global approach with rising strings providing the tension and the surrounding ambience slowly dipping out so you become more focused on the dialogue. Or any other way you can think of.
In terms of whether this affects the kind of story it is, I guess that’s up for debate but I think no. The story is already written, sound is one of the ways in which the story is realised. I once worked on a short animated film where for some reason we decided not to follow direction and made it a lot darker than intended. The animation team liked it so much it stuck - did that change the story? Not really, but I guess it changed the subtext and the way in which the story was told.
Hope that helps, just my thoughts :)