Poetry is a form of writing in verse, which usually has a musical quality obtained through the specific use of literary elements such as meter and rhyme, and literary devices such as alliteration, onomatopoeia, and other vivid forms of imagery. A short story has characters of depth, and a plot that centers, generally, around a conflict of some sort. The two are different in that poems don't have to tell a story and can be about a single brief idea, whereas a short story generally is the exact opposite; but both can convey deep meaning to the audience, often eliciting an emotional response, through the author's careful use of the language as he/she shares a message through writing.

In addition to the above posts, I think even narrative poetry uses more "poetic license" than short stories.  Though many fiction writers get away with the use of sentence fragments or punctuation irregularities, for example, it seems it is a little more widely done (and accepted) with poetry.

We always recognize that authors and poets make intentional choices when they write, but it would seem that poets have more pressure to make it just right.  Because a traditional-type poem is concise, it must also be precise.  The connotation of each word, the signficance of the sounds of words together, the length of the line, the structure of the stanzas (or lack there-of) is only a short list of how everything matters in a poem.

I want to second the point made by ask996 and add to it. Poetry and short stories may seem very different at first glance, but the differences aren't always easy to piin down. Poems can be very long and/or tell stories, for example, just as short stories can have very lyrical qualities. Edgar Allan Poe's famous comments about the "single effect" of shorter literary works (including most poems and most or all short stories) in "The Philosophy of Composition" seems to suggest that the two may have more commonalities than differences.

The differences become particularly difficult to pin down when writers seek to blur the boundaries, writing things that might best be described as "prose poems." Jean Toomer's Cane is one of the best (if not widely read today) examples, I think.

I thnk one of the best points made so far is accessteacher's comment about the "condensed meaning" in poetry.

Both short stories and poetry use the previously mentioned literary techniques mentioned above. I would like to add, however, that their are some forms of poetry that do not focus on things such as rhyme and meter. Free verse does not rely on established meter, blank verse has an unrhymed meter that more closely resembles natural speech, and narrative poetry tells a story.

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.

A poem attempts to say the most by saying the least.  Poets have certain methods at their disposal, such as symbolism, rhyme, meter, personification, and many others.  A short story, on the other hand, still attempts to convey a theme, but often seems to utilize different techniques, such as setting, tone, characterization, etc.

These two different literary forms share much in common, however, so each of them may "borrow" or "adopt" other strategies in order to maximize the impact of the message.

One of the greatest differences between poetry and a short story is that it always evokes an emotional response from the reader.  This response is generated in the reader of poetry because of the rhythm of the lines, the superb and exact choice of words, and the figurative language which touches upon the very spirit and heart of the reader. Even the  visual appearance of a poem can delight the reader as often poet's arrange a poem to fit the subject

Poetry, too, is often read aloud--and should be.  When the reader speaks the words, there is that communication between the poet and the reader which does not often occur with a narrative that is usually read silently.

This is a great question to ask and think through. One suggestion I will make is that you post this on the discussion board for literature as you will gain far more responses than if you merely post it as a question.

For me, one useful way of defining poetry is as "condensed meaning." It is literally like a message or a theme that has been condensed into a very small form, but which must be "unpacked" to appreciate the full significance of what the author is trying to communicate.

Short stories are of course shorter than novels, and so they share many similarities with poetry. In both the authors try to get the message across with brevity and in a succinct form. However, poetry achieves this in the extreme - often only a couple of stanzas can be enough to communicate an incredibly complex theme or idea. In poetry authors do not have the luxury of spending time establishing theme and character - they must say what they want to say in as sparse a form of language as possible.