beginning rhyme vs rhyme

beginning rhyme and rhyme both are nouns.

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

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

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

Other hypernyms of beginning rhyme include rime.

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

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