arm exercise vs chin-up

arm exercise and chin-up both are nouns.

Word	Noun	Adjective	Verb	Adverb
arm exercise	Yes	No	No	No
chin-up	Yes	No	No	No

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

arm exercise: exercise designed to strengthen the arm muscles
chin-up: an arm exercise performed by pulling yourself up on a horizontal bar until your chin is level with the bar

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

arm exercise (noun)	chin-up (noun)
exercise designed to strengthen the arm muscles	an arm exercise performed by pulling yourself up on a horizontal bar until your chin is level with the bar