What term describes the order in which the poem or story rhymes?

The term that describes the order in which the poem or story rhymes is "rhyme scheme." Rhyme scheme refers specifically to the pattern of end sounds in lines of poetry, often represented by letters to denote which lines rhyme with each other. For example, in a quatrain where the first and third lines rhyme and the second and fourth lines rhyme, the rhyme scheme would be labeled as ABAB.

While "rhyme" refers to the repeating sound that creates rhythm and musicality in poetry, it does not specify the organization or pattern of those sounds. Terms like "pun" and "oxymoron" refer to specific figures of speech and wordplay, which are distinct from the concept of rhyme scheme. Therefore, "rhyme scheme" is the most accurate term to use when discussing the structured arrangement of rhymes in a poem or story.