force vs push

force and push both are nouns.

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

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

force: (physics) the influence that produces a change in a physical quantity
push: the force used in pushing

As verbs, force and push are synonyms defined as:

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

force (noun)	push (noun)
a putout of a base runner who is required to run; the putout is accomplished by holding the ball while touching the base to which the runner must advance before the runner reaches that base	the act of applying force in order to move something away
an act of aggression (as one against a person who resists)	an effort to advance
physical energy or intensity	an electrical switch operated by pressing
a powerful effect or influence	enterprising or ambitious drive
(of a law) having legal validity	the force used in pushing
group of people willing to obey orders
a unit that is part of some military service
a group of people having the power of effective action
one possessing or exercising power or influence or authority
(physics) the influence that produces a change in a physical quantity

force (verb)	push (verb)
impose urgently, importunately, or inexorably	make publicity for; try to sell (a product)
squeeze like a wedge into a tight space	press, drive, or impel (someone) to action or completion of an action
force into or from an action or state, either physically or metaphorically	make strenuous pushing movements during birth to expel the baby
take by force	move with force
do forcibly; exert force	approach a certain age or speed
urge or force (a person) to an action; constrain or motivate	press against forcefully without moving
move with force	move strenuously and with effort
to cause to do through pressure or necessity, by physical, moral or intellectual means	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