arm exercise vs pushup

arm exercise and pushup both are nouns.

Word	Noun	Adjective	Verb	Adverb
arm exercise	Yes	No	No	No
pushup	Yes	No	No	No

As nouns, pushup is a hyponym of arm exercise; that is, pushup is a word with a more specific, narrower meaning than arm exercise:

arm exercise: exercise designed to strengthen the arm muscles
pushup: an arm exercise performed lying face to the floor and pushing the body up and down with the arms

Other hyponyms of arm exercise include press-up, chin-up, pull-up.

arm exercise (noun)	pushup (noun)
exercise designed to strengthen the arm muscles	an arm exercise performed lying face to the floor and pushing the body up and down with the arms