I define story as a narrative of events (external or psychological) which moves through time or implies the passage of time, and which involves change.
It took a lot longer for me to be able to define plot and tell it apart from story. Part of the problem was that I kept coming up against that well known E M Forster quote and, lo, it's cropped up again in the course material for the on-line creative writing course I tutor, namely:
Block 1 explained plot very briefly, with the help of E.M. Forster’s example: 'The king died and the queen died' is a story. 'The king died and then the queen died of grief' is a plot.
And yet again, a little voice in my head wailed, "Noooooo! 'The king died and the queen died' is merely a string of incidents." What I would call story is what Forster calls plot. But I've always had to grit my teeth and keep silent, for who am I to argue with E M Forster?
But now at last I have an ally. Joan Aiken in her book The Way to Write for Children says:
But what E.M.F. refers to so disparagingly as a story is, in fact, not a story at all, but a mere narrative. His definition of plot is what I would call a story: 'The king died, and then the queen died of grief.'
So, as the creative writing course materials do go on to say, "...a plot is a narrative of events, with the emphasis on causality." (my emphasis) or, as Ursula Le Guin puts it:
I define plot as a form of story which uses action as its mode, usually in the form of conflict, and which closely and intricately connects one act to another, usuually through a causal chain, ending in a climax.
Or to put it another way, the plot supports the story, like a skeleton for the narrative; because as LeGuin also says, "Most serious modern fictions can't be reduced to a plot or retold without fatal loss except in their own words. The story is not in the plot but in the telling. It is the telling that moves."