quatrain

As nouns the difference between quatrain and kyrielle

is that quatrain is a poem in four lines while kyrielle is a long rigmarole.

As nouns the difference between quatrain and pantoum

is that quatrain is a poem in four lines while pantoum is a poem, similar to a villanelle, that comprises a series of quatrains, the second and fourth lines of each stanza repeated as the first and third lines of the next.