rhyme vs initial rhyme

rhyme and initial rhyme both are nouns.

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

As nouns, initial rhyme is a hyponym of rhyme; that is, initial rhyme is a word with a more specific, narrower meaning than rhyme:

rhyme: correspondence in the sounds of two or more lines (especially final sounds)
initial rhyme: use of the same consonant at the beginning of each stressed syllable in a line of verse

rhyme (noun)	initial rhyme (noun)
correspondence in the sounds of two or more lines (especially final sounds)	use of the same consonant at the beginning of each stressed syllable in a line of verse
a piece of poetry

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