push vs promote

push is a noun but promote is not a noun.

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

As verbs, push and promote are synonyms defined as:

Other synonyms of push include advertise, advertize.

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

push: 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
promote: make publicity for; try to sell (a product)

Other hypernyms of push include advertise, advertize, push.

push (noun)	promote (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)	promote (verb)
make publicity for; try to sell (a product)	make publicity for; try to sell (a product)
press, drive, or impel (someone) to action or completion of an action	change a pawn for a better piece by advancing it to the eighth row, or change a checker piece for a more valuable piece by moving it to the row closest to your opponent
make strenuous pushing movements during birth to expel the baby	be changed for a superior chess or checker piece
move with force	give a promotion to or assign to a higher position
approach a certain age or speed	contribute to the progress or growth of
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