What is the difference between poetry and prose?

I believe that anyone who knows wouldn't ask and the rest wouldn't know to ask. And yet, answering the question carries with it a sort of immensity that is at once enticing and annoying.
Let's begin by setting aside certain features of language. Ordinary talk between ordinary people uses ordinary language. Verbs do what verbs do; nouns do what nouns do. This is what we learned in grade school. So, we set aside certain features of language. Rhyme, for example, is a quintessentially poetic feature of language and rarely do we use in ordinary language; when we do, we laugh because it sounds so unnatural. And, yet, when used purposefully, when called to the foreground of an incident of language, rhyme takes on the dimensions of beauty. We have, of course, stepped from mere language into realm of literature.
Poetry and prose overlap considerably. There are, in fact, great traditions of poetic prose and prose poetry, so, on some level, it's foolish to imagine that there's a clear cut difference and never the twain shall meet. A scale must be properly drawn between them on which tendency associate towards one of the other. Organization of language (such as into stanzas) tends to associate with poetry, but there are, of course, exceptions. Lines, too, tend towards poetry; sentences toward prose. Meter tends toward poetry, but not extremely so. Metaphor, for example, is not commented on by the scale; it is accessible to both. And so on.
Poetry versus Prose
Poetry refers to poems, with or without rhyme schemes. Prose is writing a story,either fiction or nonfiction. Poetry and prose are both forms of expression in writing. Prose usually has fewer structural guidelines, and in some ways, that makes poetry more of an art form. Being able to express the same thought and image in fewer words, choosing more carefully, etc., makes poetry more difficult to master than prose.
Poetry has rhythm, like a song. Poetry has cadence, like a drum. Poetry may rhyme but, I'm not wrong, When I say it can be ho hum.
Poetry usually follows a set pattern, rhyme scheme and meter. It is an art form in which human language is used for its aesthetic qualities. Prose is simply regular writing, like in a story, a letter, or regular speech. There are usually no patterns, just sentences and paragraphs.
Prose writing most often follows standard rules in grammar, punctuation, capitalization, and sentence structure. Poetry often doesn't, for expressive reasons, and every word, period, etc. is carefully chosen to say the most using the least words.
Prose is the language of everyday speech, or the writing medium that mimics it. Poetry is a more refined or structured or rhythmic form of prose.
Poetry has a shrinking readership. This is mainly because of competition from other media, but partly because poetry written in the last 50 years is perceived to have not been up to past standards.
On the other hand, there is a lot of modern poetry that is quality. Whether or not the readership is going down in some circles, there are remarkable poets who have been active during the last 50 years, and hopefully will continue to be.
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Many definitions exist for poetry and for prose, and the characteristics are very blended and the border between them made very grey - the above answers are all correct, in a way.
I, however, think that the difference between poetry and prose is that poetry ought to be written linearly whereas prose is that which is to be structured into paragraphs. Coleridge defined poetry as "the right words in the right order" and my father always said "maximal meaning in minimal wording", but I would reckon that this line/paragraph differentiation is the best way to separate.