What to you is the difference between the narration of sequential events and a story?
Daniel Kahnemann would say, causal attribution.
"This, then that, then that, and then that" is a random sequence of events.
"This, and then, so that, but then" is a story.
Of course that doesn't mean a story can't have a place for random elements. Deus ex machina tends to get eyerolls nowadays, but that's not to say that something employing this device is less of a story.
Still, even deus ex machina is random only on a surface level. If the god from the machine saves the deserving, it's poetic justice. If he helps evil triumph, that's because its victims were too pure for this world. If it's rocks fall, everyone dies, we'll find some deeper reason for that too.
Because the truth is, we'll read the 'so"s and "but"s, whether the author spells them out or not. The story is made by the reader, and the reader can't help it. That's just how our mind works.
(I've got a degree in English, I can read a story into a grocery list. Someone else might need a bit more priming to trigger story mode, but something as simple as starting with 'once upon a time" would probably do. Title it 'story", and your readers will see it as a story. They might not find it terribly plausible, or compelling, but they"ll see it allright. Not seeing is would be the harder feat.)
Of course, Daniel Kahneman is psychologist, not a writer of fiction. Still, I couldn't think of anything to add.
I'm currently reading 'Thinking Fast and Slow' about how people generally don't get statistics, because our mind just isn't set up to handle this form of information. We either process it as a story (inevitably distorting the facts, by adding sos and buts where there are none), or we won't process it at all.
At a competition, ski jumpers jump twice, and you can notice a pattern: if they excelled at the first jump, the second one will be worse. If the fucked up the first jump, they second one will be better.
Of course the announcers have noticed that, and the make the corresponding predictions: he did very well at the first jump, now the expectations are raised, they will tell you, he will get nervous and we should expect him to do worse in the next round. Or, she missed the sweet spot, but at at least now the pressure is off, watch her soar the next time. That's a story.
Daniel Kahnemann would say, of course, the excellent first jump had a great element of luck in it (and the messed up first jump a great element of bad luck), and there's no reason whatsoever to assume that random element will remain the same for the next round, so the most likely outcome is regression to the mean. That's statistics.
And that second way of thinking, it doesn't come naturally. Kahneman has a whole chapter about how long it took scientists to figure out regression to the mean, and how they often they still forget about it, in spite of having taking all the required statistics classes at some point. We generally don't know how to make sense of facts without turning them into a story.
In conclusion, a story is anything that makes some sort of sense.
What makes some stories more powerful than others, however, that's another question.