push vs agitate

push is a noun but agitate is not a noun.

Word	Noun	Adjective	Verb	Adverb
push	Yes	No	Yes	No
agitate	No	No	Yes	No

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

push: make publicity for; try to sell (a product)
agitate: exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for

Other hyponyms of push include propagandise, propagandize, plug, bill, campaign, crusade, fight, press, push.

As verbs, push and agitate are synonyms defined as:

push and agitate: exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for

Other synonyms of push include campaign, crusade, fight, press.

push (noun)	agitate (noun)
the act of applying force in order to move something away
an effort to advance
an electrical switch operated by pressing
enterprising or ambitious drive
the force used in pushing

push (verb)	agitate (verb)
make publicity for; try to sell (a product)	change the arrangement or position of
press, drive, or impel (someone) to action or completion of an action	cause to be agitated, excited, or roused
make strenuous pushing movements during birth to expel the baby	move very slightly
move with force	move or cause to move back and forth
approach a certain age or speed	try to stir up public opinion
press against forcefully without moving	exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for
move strenuously and with effort
sell or promote the sale of (illegal goods such as drugs)
strive and make an effort to reach a goal
exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for