Rhymes depend on matching words with identical sounds, either vowel sounds or, frequently, combinations of vowels and consonants. Rhyming pairs can be single-syllable words, such as "blue/threw," or multisyllabic, such as "crying/sighing," "critical/analytical" or "motionless/oceanless." Assonance, on the other hand, depends on matching only vowel sounds within words, such as in the phrase "high and mighty," which repeats the long "I" sound, or "days of rage," which repeats the long "A." Assonance applies only to vowel sounds. Repeating consonant sounds within words--"fine and dandy"--is a related device, called consonance. When it occurs at the beginning of the words--"pretty punctual"--it's alliteration.
Rhymes occur with terminal sounds--the sounds at the end of words. "Whose" and "dune" have nearly identical vowel sounds, but the words don't rhyme, because the terminal consonant sounds are different. Assonance can occur within words just as easily as at the ends; the consonants before and after the assonant vowels don't really matter. The point is to create an almost musical flow within a phrase or group of words. Phrases such as "on a moment's notice" or "line drive" or "Mile High City" draw their impact from assonance.
Rhymes act as a kind of punctuation that helps match lines of verse. A seldom-sung stanza from "America the Beautiful" provides a typical example: "O beautiful for patriot dream/that sees beyond the years/Thine alabaster cities gleam/ undimmed by human tears." Rhyming pairs create matches between the first and third lines and between the second and fourth lines. Assonance is more typically used to create flow within individual lines of prose or verse. A line from Edgar Allen Poe's "The Raven" demonstrates the effect: "It shall clasp a sainted maiden whom the angels name Lenore." This line has three assonant pairs: "shall clasp," "sainted maiden" and "angels name."
Assonance can, and often does, stand in for rhyme in music and poetry. Song lyrics might match such words as, say, "sit" and "ship." While not a "true" rhyme, the words are close enough that the listener accepts them as a rhyme. There's even a term for it: assonant rhyme. Of course, such distinctions mean little to a listener or reader enjoying a song or poem. Alberto Alvaro Rios, an acclaimed poet and professor of English at Arizona State University, warns against getting hung up on drawing lines between such concepts. These terms are useful to the writer, he says, but mean little to the reader.