A short story tells a story through use of character, theme, dialogue, motif, setting, tone, and narration. It is typically wordier than a poem, although the two have brevity in common.
Both a short story and poem attempt to cut out anything that is not needed to convey the author's purpose. However, a poem is even more brief than a short story. It has a speaker, a voice who tells its story in as few words as possible, usually focusing on imagery, emotion, and other poetic techniques such as onomatopoei, figurative language, tone, mood, and stanzas rather than paragraphs.