arm exercise vs exercise

arm exercise and exercise both are nouns.

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

As nouns, exercise is a hypernym of arm exercise; that is, exercise is a word with a broader meaning than arm exercise:

Other hypernyms of arm exercise include exercising, physical exercise, physical exertion, workout.

arm exercise (noun)	exercise (noun)
exercise designed to strengthen the arm muscles	the activity of exerting your muscles in various ways to keep fit
	a task performed or problem solved in order to develop skill or understanding
	systematic training by multiple repetitions
	the act of using
	an action, often used negatively and without consequences
	(usually plural) a ceremony that involves processions and speeches

arm exercise (verb)	exercise (verb)
	do physical exercise
	give a workout to
	learn by repetition
	put to use
	carry out or practice; as of jobs and professions