You might find the Wikipedia explanation of plot more helpful. A plot, in the sense that you mean it, is a part of certain types of stories. An author may create the plot before actually writing a story to explain to someone else what she intends to write or as sort of an outline to assist her in writing the story.
This may be a strange illustration, but the Angry Alien Productions website has "30-second Bunnies Theatre" videos in which the plot of a full length movie is re-enacted in 30 seconds. The movie is the story, and the 30 second re-enactment is the plot (or at least as many of the most memorable parts of the plot that will fit into 30 seconds).
A story may be fictional or not. A plot is a sequence of events planned by the author of a story. A plot could be based on a non-fictional story, but it is usually manipulated to make the story more compelling or dramatic.
I could tell stories about my trip to Europe that don't have a plot - they are just events that happened to me as I was travelling. If I wrote a play based on my trip to Europe, I would probably create a plot using those events that would give them more meaning and link them together so that my audience would stay interested. I might omit some things that happened because they aren't important to the plot of the story that I want to tell.