rhyme vs versification

rhyme and versification both are nouns.

Word	Noun	Adjective	Verb	Adverb
rhyme	Yes	No	Yes	No
versification	Yes	No	No	No

As nouns, versification is a hypernym of rhyme; that is, versification is a word with a broader meaning than rhyme:

rhyme: correspondence in the sounds of two or more lines (especially final sounds)
versification: the form or metrical composition of a poem

rhyme (noun)	versification (noun)
correspondence in the sounds of two or more lines (especially final sounds)	the art or practice of writing verse
a piece of poetry	the form or metrical composition of a poem
	a metrical adaptation of something (e.g., of a prose text)

rhyme (verb)	versification (verb)
compose rhymes
be similar in sound, especially with respect to the last syllable