In conversation almost everybody uses the words plot and story interchangeably. They might as well mean the same thing.
However, literary scholar Humphry House made a really helpful distinction between the two. For House, story is all of the events the reader needs to make sense of the plot. Plot, on the other hand, is what the writer chooses to display.
Take Harry Potter and the Sorcerer’s Stone, for example. The plot begins when McGonagall, Dumbledore, and Hagrid drop newly-orphaned Harry Potter off at number Four Privet Drive. The plot then jumps ten years forward to just about Harry’s eleventh birthday.
Using House’s distinction, the story is a little different. The story of Sorcerer’s Stone doesn’t begin with Harry getting dropped off at Aunt Petunia’s. The story doesn’t even begin with Voldemort murdering Harry’s parents. The story begins years and years prior, probably going back to the time of Tom Riddle. Portions of Voldemort’s backstory (i.e. part of the story that contributes to the plot but isn’t shown to the reader) are super important in understanding the book.
The ten-year time jump also contains a lot of story, but it doesn’t directly contribute to the momentum of the narrative. The reader needs to understand that Harry has suffered growing up in Aunt Petunia’s house, but J. K. Rowling made the authorial decision not to show the reader those ten years. Why? Because it would be boring and there’s probably very little to do with Voldemort or Hogwarts or cool stuff in that decade.
In Aspects of the Novel, E. M. Forster takes this idea a step farther, saying a story is: “…a narrative of events arranged in their time sequence. A plot is also a narrative of events, the emphasis falling on causality. ‘The king died, and then the queen died,’ is a story. ‘The king died, and then the queen died of grief,’ is a plot.”
No author would ever do this, but imagine Rowling hadn’t plotted Sorcerer’s Stone the way she did. Imagine the plot was the exact same as the story. Rowling would begin years before Harry was born and cover, essentially, every event of his young life leading up to his confrontation with Voldemort. Not only would this be insanely long and boring, it would also entirely lack drama.
We regular people always plot our stories in daily life. It’s how you make a series of events interesting. Let’s say you almost get hit by a car on your way to work. You’d decide whether you begin the story at the end (“I almost got hit by a car today!”) or start with your way to work (“So I woke up this morning, and headed to work…”). Which is more interesting? You’d probably get your mom (or whoever’s listening) hooked if you start with the biggest source of conflict, which is the near accident.
Anyway, although the two might commonly be used as synonyms, it’s helpful to learn and recognize their differences. Once you’ve internalized their different definitions, you can start to see how and why a writer makes the choices they make. Pretty freaking exciting!