The play, Trifles, and the short story,"A Jury of Her Peers," both by Susan Glaspell, are the same story told through a different medium. As such, there is little variation between them. The dialogue retains a nearly word-for-word similarity, and the narration in the story closely coincides with the stage instructions in the play. The two main differences are that Martha Hale's perspective and feelings become the primary point of view in the short story and that in the short story Glaspell emphasizes the importance of the evidence the women find, making it clear that they know exactly what they are doing. 

The story begins with Mrs. Hale at her house, preparing to ride by wagon to the Wrights's with Sheriff Peters and his wife. Readers get a glimpse into her backstory that they do not get in the play. Throughout the story, Glaspell tells the reader what Mrs. Hale is thinking. In the play, viewers must surmise from characters's actions, words, and expressions what is in their minds. Readers understand Mrs. Hale's skepticism about Mrs. Peters and her growing trust that the woman understands Minnie's plight. 

Three parts of the story serve to emphasize the import of the women's act of withholding evidence. First, when the county attorney tells Mrs. Peters to keep an eye out for any useful evidence, he adds this line that does not appear in the play: "No telling; you women might come upon a clue to the motive—and that's the thing we need." The play hints at this—that what is necessary to convict Minnie Wright is something to show motive—but it is not as heavy-handed as in the story. Second, when Mrs. Hale laments to Mrs. Peters that she should have known Mrs. Wright needed help, this line is added in the story that is not in the play: "If it weren't—why do you and I understand? Why do we know—what we know this minute?" Again, this makes it unavoidably clear that the two women know Mrs. Wright murdered her husband and why. Finally, the story drives the point fully home when the dead canary is referred to as "the thing that would make certain the conviction of the other woman." This makes sure the reader knows how crucial the evidence is that the women withhold. 

Although the story and play are very similar, Glaspell uses the short story medium to clarify the decision the women make so that the two women bear full responsibility for the leniency that will certainly be shown to Mrs. Wright. They play the role of Mrs.Wright's jury, and the reader is left to grapple with whether the women were justified in interfering with the legal system.

There is more authorial intrusion in the short story "A Jury of Her Peer" than in the play Trifles. As such, Glaspell reveals many more of her characters' feelings in the short story.  She leaves the emotional subtext for the actors to reveal on stage.

So says one critic:

For example, on page 275 the writer explains how Mrs. Hale first met Mrs. Peters, “the year before at the county fair”. Mrs. Hale’s opinion of Mrs. Peters is brought to the surface on page 276 when the writer reveals that she felt Mrs. Peters “didn’t seem like a sheriff’s wife”. Whereas in the play Trifles, the reader is left with no insight of this nature since the dialogue is so central (all you know is what you see and hear). Feelings are left out of the play, and revealed in the short story.

Another obvious difference is the title. The play's title Trifles is more subtle, whereas the short story's title "A Jury of Her Peers" basically reveals two major themes from the start: feminist community ("her Peers") and legalism ("Jury").  Trifles is wonderfully ironic: it is what the men think of women's work.  As such, its title better reveals the little things (the clues and subtext), which drives this psychological play.

The women are marginalized more in the play. They are physically segregated from the men, and their presence on stage keeps them--as a community--front and center.  No one woman is more important than the other.  Even though it is titled Trifles and not "A Jury of Her Peers," the play's grouping of the women allows them to be more of a physical jury.  This is more symbolic and meaningful.

Audience participation, I feel, is the biggest difference. Quite frankly, the short story gives too much away.  It's too easy, too seamless.  The play, even if it is read and not seen, is much more like a detective story.  As a reader or viewer of the play, we have to use more deductive reasoning and fill in the pieces to the mystery.