Story and plot. In common usage, we use these two terms interchangeably, making no real distinction between one and the other. But in formal literary studies, story and plot are two subtly different concepts. Understanding their differences can help you tell more engaging tales.
Story is the straightforward account of what happened. It is the essential core, the most basic idea, the simplest framework on which everything hangs. A story you can sum up in one or two sentences because you already take out all the embellishments.
Plot, on the other hand, is the presentation of the story. It is the sequence of events by which you unfold a tale in order to maximize suspense and delight. If story is the skeleton, plot is the guts, muscle, and skin. Plot is what makes a story interesting.
To better understand the distinction between story and plot, let's dissect a well-known example, "Star Wars: A New Hope."
What is the story of "A New Hope"? If you strip it down to its bare essentials, it's about a simple farmboy who rescues a princess and kills the dark lord threatening the kingdom (or the galaxy, in this case.) And there you have the core. It's not very interesting but that about sums it up. It's also the story of many a typical fairy tale.
Where things get interesting is when the plot comes in. What is the plot of "A New Hope?" It starts not with the farmboy but with the princess. The princess is on the run but is captured by the dark lord. She manages to send out a call for help to an old wizard. The call finds its way to the farmboy, who passes it on to the wizard. The wizard enlists and trains the farmboy. They smuggle themselves to the kingdom with the help of a lovable rogue, only to be captured by the dark lord. They escape and rescue the princess. The wizard dies while securing their escape. They assemble a desperate army and, against all odds, defeat the dark lord.
Note that the plot follows the basic story but manages to introduce some twists and turns that make it slightly different from other stories in the presentation, e.g., the help of the lovable rogue and the sacrifice of the wizard. It is in the plot where you have a clear beginning and a clear end; and in between, you get to play with the essential storytelling question: "what happens next?"
Plot-wise, "A New Hope" follows a linear sequence. It doesn't necessarily have to be so. Plot can incorporate flashbacks or flash forwards, or even sideways digressions. By rearranging the plot, you can even tell a story backwards. Anything goes, but the point is to make the story interesting in the presentation.
Plot also affects story. As you add more elements, you might find yourself telling a different story. Going back to our Star Wars example, if you interconnect "A New Hope" with its companion pieces in the original Star Wars trilogy, "The Empire Strikes Back" and "Return of the Jedi", it becomes something else. The original trilogy now becomes the story of a boy who turns his father from evil back to good.
If you expand the Star Wars plot to include all six films, the focus shifts away from the farmboy Luke to his father Anakin. It's now the story of how an ambitious young man turns to evil in pursuit of power, and how he finds redemption through his son.
This distinction and relationship between story and plot has been very well studied and goes as far back as the 1920s. If you'd like to know more about this fascinating topic, you can read up on some articles on Literary Theory, in particular, the works of Boris Tomashevski and Vladimir Propp.