postulate vs assert

postulate is a noun but assert is not a noun.

Word	Noun	Adjective	Verb	Adverb
postulate	Yes	No	Yes	No
assert	No	No	Yes	No

As verbs, assert is a hyponym of postulate; that is, assert is a word with a more specific, narrower meaning than postulate:

Other hyponyms of postulate include insist.

postulate (noun)	assert (noun)
(logic) a proposition that is accepted as true in order to provide a basis for logical reasoning

postulate (verb)	assert (verb)
take as a given; assume as a postulate or axiom	postulate positively and assertively
maintain or assert	to declare or affirm solemnly and formally as true
require as useful, just, or proper	state categorically
	insist on having one's opinions and rights recognized