As the title says: what is an adventure story, truly? I realised I never had a very concrete definition.
Is it just the fact that the main characters leave to go and visit other areas and do stuff?
Or is it in what they do? The plot where they go there to get the thing, etc etc...

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If they just go and collect their MacGuffin, then it's not an adventure, it's an errand. There needs to be a twist or a false ending to the quest so as to make the adventure adventurous and intriguing.

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What makes an adventure story adventurous?
Folks doing stuff and the stakes are pretty high.

Slice of life:
Derpy goes to the bakery and gets a muffin.

Adventure:
The Muffin man and his gang of baked bads have invaded Ponyville, and now Derpy must fight her way house to house to defeat him and save the town.

Sometimes there are twists or false endings or sometimes not.
That's a style thing.

LOTR didn't have a twist or false endings.
I don't know if twists and trick endings are necessary.
That might depend on the story.