First, the difference: sound is the vibration of physical substances, perceived by the ear. Poetry is word formations (signifiers) by human beings as part of a language communication. But their similarities are remarkable.
A lot of the vocabulary used to describe and criticize poetry is metaphor taken from the physics of sound, and from music: rhythm, tone, repetition, timbre, etc. Of all the forms of literature, poetry pays the most attention to the sound of the spoken word. (Even though dramatic literature is created to be spoken aloud, the sense and the “art” of the dialogue reside primarily in denotation, speech acts, and psychological phonetics.) Such poetic devices as endrhyme and near-rhyme, cadence, alliteration, even syllable length, all depend on the assumed oral (or at least mental) recital of the work, along with symbolism, metaphor, connotation, etc. In these respects, poems are a kind of sound, the kind the human voice makes when communicating a complex, abstract idea. Music is a kind of sound also, sharing many of these same features: rhythm, tone, timbre, cadence.