work out vs weightlift

work out is not a noun while weightlift is a noun.

Word	Noun	Adjective	Verb	Adverb
work out	No	No	Yes	No
weightlift	Yes	No	Yes	No

As verbs, weightlift is a hyponym of work out; that is, weightlift is a word with a more specific, narrower meaning than work out:

Other hyponyms of work out include limber up, loosen up, warm up, train, tumble, strengthen, tone, tone up, press, weight-lift.

work out (noun)	weightlift (noun)
	bodybuilding by exercise that involves lifting weights

work out (verb)	weightlift (verb)
do physical exercise	lift weights
give a workout to
come up with
work out in detail
find the solution to (a problem or question) or understand the meaning of
make a mathematical calculation or computation
be calculated
happen in a certain way, leading to, producing, or resulting in a certain outcome, often well