push vs fight

push and fight both are nouns.

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

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

push: make publicity for; try to sell (a product)
fight: 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, agitate, campaign, crusade, press, push.

As verbs, fight is a hypernym of push; that is, fight is a word with a broader meaning than push:

Other hypernyms of push include struggle.

As verbs, push and fight are synonyms defined as:

push and fight: 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 agitate, campaign, crusade, press.

push (noun)	fight (noun)
the act of applying force in order to move something away	a hostile meeting of opposing military forces in the course of a war
an effort to advance	the act of fighting; any contest or struggle
an electrical switch operated by pressing	a boxing or wrestling match
enterprising or ambitious drive	an aggressive willingness to compete
the force used in pushing	an intense verbal dispute

push (verb)	fight (verb)
make publicity for; try to sell (a product)	be engaged in a fight; carry on a fight
press, drive, or impel (someone) to action or completion of an action	fight against or resist strongly
make strenuous pushing movements during birth to expel the baby	make a strenuous or labored effort
move with force	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
approach a certain age or speed
press against forcefully without moving
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