A popular misconception seems to be that either the two terms plot and story are synonymous or that plot describes events and story events in a chronological order. The latter is technically true, but for different reasons other than the definition of a term. Part of the reason the difference is percieved that way because of the term "plot-driven narrative". Before I go into rambling, let's structure this critter, shall we?
A plot would be:
"The wife dies, then the husband dies",
Or even more simplistic and completely without chronological order:
"A husband dies. A wife dies."
A story would be:
"The wife dies, then the husband dies of grief."
The reason a plot can be out of order is because it's just a list of events that don't depend on chronological structure when presented to the audience, thus the term "plot-driven narrative".
The story adds emotion to everything. How does A react to B's reaction? The plot might easily give a different answer than the story. For example A can remain completely silent and not react, the plot being: B does something, A remains passive. However, the story might be two of many things: B does something and A is deeply hurt/overjoyed yet remains passive.
Or let's take the monomyth, also known as the Hero's Journey:
The plot always has the same or a similar structure, but the story, which includes the characters' personalities and emotions, makes each tale unique. That is also why the Hero's Journey is the best path to follow for aspiring writers, the setting is almost interchangeably and therefore one can focus on the characters instead.
To be more specific: Their actions and journeys might be similar, but Luke Skywalker and Eragon Garrowson are not interchangeable despite being archetypical heroes and goody-goods. Why is that? Well, Eragon's emotional core is intertwined with Saphira, his dragon, a connection that Skywalker does not have, instead he has found friends in Han Solo and Chewbacca, but their relationship is nowhere near as strong as Eragon and Saphira's whose souls, deep down, are merged with the other's.
Another example: The basic plot of a lot of Batman stories is that an inmate of the worst mental institution of all time, Arkham Asylum, escapes and starts wrecking Gotham City so Batman goes and stops them. Sounds pretty repetitive, so how did the character endure for so long outside of crossovers? One part is the mythology of the bat, best explained in OanCitizen's Between the Lines video, but the other part is the emotional journey. How does the new or old threat influence the cave-dweller, and how does HE influence his antagonist(s)? Those are the interesting questions that keep the readers invested.
Another example is the most controversial of all superhero movies -no, not "The Crow", that is Urban Fantasy, not a superhero movie-: Man of Steel.
I am very vocal about my negative opinion, but so far I only expressed my dislike of the general betrayal of the character, but its greatest flaw from an objective perspective is: It has no story.
There is no emotional journey, only exposition. We get one or two lines displaying a character's personality at most, and most of the movie is fight scenes.
The plot is that the planet Krypton dies (Yeah, what a shock) and with it its population. But not the entire population. A single Kryptonian child is sent to Earth, our Earth, while treacherous soldiers along with with their general is imprisoned in the Phantom Zone, these are the only survivors. Then the militant ugenics hunt down the baby, in order to get a device that allows them to create Krypton anew out of Earth's ashes, and the baby, now a grown man, 33 years old, stops them and kills their leader while banishing the other Kryptonians via Quantum Singularity.
That is all fine and well, but there is no character to the, well, characters. The most characterization we get from any of them is General Zod, the villain. And he is a ugenics soldier, thus he is also very two-dimensional. Once all hope of a new Krypton is gone, he goes mad and all out against "Superman" who took everything from him and... That's it. He dies there. Does Superman killing have an emotional impact on him as Superman or the person behind the suit, Clark Kent? No. Because there are no consequences. Therefore the entire story is superfluous, he might just as well have thrown on the suit and said: "I am Superman now" and that could have been the end of it. Instead a plot was completed, a plot which contained all the right ingredients for a Superman story, but ended up being just a standard alien invasion plot with names and a bit of background story, also without actual characters, from the Superman mythos.
A positive example would be the first Spider-Man movie by Sam Raimi, the plot is easy to grasp:
Peter Parker gets bitten by a spider, gets spider powers, becomes Spider-man, Ben Parker dies, Spider-Man starts fighting crime and Norman Osbourne as the Green Goblin and the Green Goblin defeats himself.
The story, however, is the real meat of the movie. It is Peter Parker's coming of age, coupled with his Uncle's death teaching him that "with great power comes great responsibility" driving him to become a force of good, a masked vigilante with the proportionate powers of a spider. While all of that is happening, Norman Osbourne becomes his own undoing... Several times. His experiments are closed after he tests the serum on himself, he loses his sanity, becomes desperate for keeping his company going, up until he thinks that Spider-Man is not just the source of his problems, but also his solution. His split personality leads to him uttering the dying words: "Peter... don't tell Harry..." after impaling himself with his own glider, Peter respects his dying wish and thus, Spider-Man has a new arch enemy: Harry Osbourne, Peter's best friend. Throughout the movie Peter tries to gain MJ's affection, but when he gets it, he's already realised that his loved ones are endangered by his life as Spider-Man, which is why he distances himself, refuses a relationship.
See, far more investing than the plot alone, isn't it? By simply adding an emotional journey to the over all goofy movie with a very simple plot made it one of the best movies ever made, and it spawned one of the greatest sequels of all: Spider-Man 2, featuring Doctor Otto Octavius.
And that was way before there was a Marvel Studios, mind you, since other than providing the mythos and a Stan Lee cameo, Marvel was not involved.
So, that were my rambling thoughts. Feel free to share your own, I'll read them all.