I'll be glad to offer a simple explanation, boiled down from Wikipedia:
"Canon" is what the author wrote.
Because the author wrote both the New Yorker Version, AND the Close Range version (Close range contains some other changes besides the prologue), both stories may be considered equally "canonical." As Leslie's link points out, Annie Proulx was NOT happy about the New Yorker leaving off the prologue because it was very important to her, thematically.
In terms of the screenplay, there are also two screenplays. I have them both if anyone wants copies.
Fan fiction is written by other authors using the original author's characters, setting, and often some of the plot.
That should clear up the terms for anyone - so by the definition of "canon", there would be both short story versions, as well as both screenplays, though the second screenplay would be more authoritative since that contained the actual shooting script from which the film was made.