term vs categorem

term and categorem both are nouns.

Word	Noun	Adjective	Verb	Adverb
term	Yes	No	Yes	No
categorem	Yes	No	No	No

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

term: one of the substantive phrases in a logical proposition
categorem: a categorematic expression; a term capable of standing alone as the subject or predicate of a logical proposition

Other hyponyms of term include subject, predicate, referent, relatum, categoreme, major term, minor term, middle term.

term (noun)	categorem (noun)
(architecture) a statue or a human bust or an animal carved out of the top of a square pillar; originally used as a boundary marker in ancient Rome	a categorematic expression; a term capable of standing alone as the subject or predicate of a logical proposition
any distinct quantity contained in a polynomial
a word or expression used for some particular thing
one of the substantive phrases in a logical proposition
(usually plural) a statement of what is required as part of an agreement
a limited period of time
the end of gestation or point at which birth is imminent

term (verb)	categorem (verb)
name formally or designate with a term