Answer:
There isn't a lot of difference, and I suppose it mostly depends on how one might use the term "story" or "article".
Explanation:
When talking about the media, we use both terms '<em>news story</em>' and '<em>news article</em>'. I guess technically, news stories refer to a story about an event, like a collision or maybe some crime, while news articles might be about why your pet shouldn't be vegan. Articles I guess tend to be more informative about a certain topic, rather than recounting an event.
Regarding books or material we find online: I'd say that a story can be true, fiction, or a mix of both. Again, usually articles are informative, and most always true.
I hope this clears stuff up for you! Feel free to leave any questions in the comments :)