The essential difference between fiction and drama as genres was first articulated in Plato's Republic and then fleshed out in Aristotle's Poetics, despite fiction per se not having been invented (the generic distinction for Plato would have been epic vs. drama). Drama uses imitation by means of direct mimesis -- actors in stage pretend to be characters -- whereas fiction and epic imitate their objects by means of a mixture of diegesis (exposition or narration in the voice of a person talking about the action) and direct imitation.
In antiquity, both epic and drama used verse rather than prose. The presence of meter only became central to the concept of genre with the invention of the ancient novel in the second sophistic. After the invention of extended fictional prose narrative, literary genres began to be distinguished by rhythmical form as well as mode of imitation:
Drama: in verse or prose is still defined as a mimetic genre
Fiction: is prose narrative
Epic: long narrative poems
Lyric: shorter, often non-narrative poems
That's a very general question, but basically speaking, a short story is a short piece of fiction that generally includes the following elements: setting, characters, point of view, theme and plot.
The basic elements of poetry are the speaker, the use of lines and stanzas, rhythm and meter, rhyme, sound devices (alliteration, consonance, assonance and onomatopoeia), imagery and figures of speech (simile, metaphor and personification).
A drama is literature which is written to be performed, and therefore, the story is generally told through the words and actions of actors. The key elements of drama include characters, setting, plot, dialogue, and acts and scenes (as divisions of the drama).
This is a summary of information from the textbook "Literature: The Reader's Choice, Course 5," by Glencoe/McGraw-Hill, 1990.
Hope this helps. Good luck!
Referring to drama in the sense of a theatrical play, drama takes on a different dimension from the others. Playwriting differs from the short story and novel in that its structure separates the dialogue to each specific character. It also includes stage directions and other specific notes that are meant for the actor/reader but are not verbally communicated on stage. Poetry differentiates from the other forms in its structure, which is usally written in separate lines and stanzas. Poetry can be free verse or rhyming verse, and it is generally the most condensed form of all. Poems tend to be based on a single thought or event, with deliberate attention to a restrictive or specific sparsity of words. A short story is a more condensed style (usually of 30 pages or less) of writing, usually--but not always--depicting a story line that takes place over a limited time period. Short stories,can also be dramatic. Dramatic elements can occur in most literary styles--novels, short stories, plays and even poetry. Dramatic elements usually involve some form of action and conflict.