exercise vs loosen up

exercise is a noun but loosen up is not a noun.

Word	Noun	Adjective	Verb	Adverb
exercise	Yes	No	Yes	No
loosen up	No	No	Yes	No

As verbs, loosen up is a hyponym of exercise; that is, loosen up is a word with a more specific, narrower meaning than exercise:

exercise: do physical exercise
loosen up: make one's body limber or suppler by stretching, as if to prepare for strenuous physical activity

Other hyponyms of exercise include limber up, warm up, train, tumble, strengthen, tone, tone up, press, weight-lift, weightlift.

exercise (noun)	loosen up (noun)
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

exercise (verb)	loosen up (verb)
do physical exercise	become less tense, rest, or take one's ease
give a workout to	cause to feel relaxed
learn by repetition	make one's body limber or suppler by stretching, as if to prepare for strenuous physical activity
put to use	cause to become unblocked
carry out or practice; as of jobs and professions	become less tense, less formal, or less restrained, and assume a friendlier manner