rhyme vs doggerel

rhyme and doggerel both are nouns.

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

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

Other hyponyms of rhyme include clerihew, doggerel verse, jingle, limerick.

rhyme (noun)	doggerel (noun)
correspondence in the sounds of two or more lines (especially final sounds)	a comic verse of irregular measure
a piece of poetry

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