push back vs force back

push back is a noun but force back is not a noun.

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

As verbs, push back and force back are synonyms defined as:

Other synonyms of push back include beat back, drive, repel, repulse.

push back (noun)	force back (noun)
the act of forcing the enemy to withdraw

push back (verb)	force back (verb)
cause to move back by force or influence	cause to move back by force or influence