vowel rhyme vs rime

vowel rhyme and rime both are nouns.

Word	Noun	Adjective	Verb	Adverb
vowel rhyme	Yes	No	No	No
rime	Yes	No	Yes	No

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

vowel rhyme: the repetition of similar vowels in the stressed syllables of successive words
rime: correspondence in the sounds of two or more lines (especially final sounds)

Other hypernyms of vowel rhyme include rhyme.

vowel rhyme (noun)	rime (noun)
the repetition of similar vowels in the stressed syllables of successive words	correspondence in the sounds of two or more lines (especially final sounds)
	ice crystals forming a white deposit (especially on objects outside)

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