class vs taxonomic category

class and taxonomic category both are nouns.

Word	Noun	Adjective	Verb	Adverb
class	Yes	No	Yes	No
taxonomic category	Yes	No	No	No

As nouns, taxonomic category is a hypernym of class; that is, taxonomic category is a word with a broader meaning than class:

Other hypernyms of class include taxon, taxonomic group.

class (noun)	taxonomic category (noun)
education imparted in a series of lessons or meetings	animal or plant group having natural relations
elegance in dress or behavior
a collection of things sharing a common attribute
people having the same social, economic, or educational status
(biology) a taxonomic group containing one or more orders
a body of students who are taught together
a body of students who graduate together
a league ranked by quality

class (verb)	taxonomic category (verb)
arrange or order by classes or categories