cocci vs true bacteria

cocci and true bacteria both are nouns.

Word	Noun	Adjective	Verb	Adverb
cocci	Yes	No	No	No
true bacteria	Yes	No	No	No

As nouns, true bacteria is a hypernym of cocci; that is, true bacteria is a word with a broader meaning than cocci:

cocci: any spherical or nearly spherical bacteria
true bacteria: a large group of bacteria having rigid cell walls; motile types have flagella

Other hypernyms of cocci include eubacteria, eubacterium.

cocci (noun)	true bacteria (noun)
any spherical or nearly spherical bacteria	a large group of bacteria having rigid cell walls; motile types have flagella