exercise vs weightlift

exercise and weightlift both are nouns.

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

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

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

exercise (noun)	weightlift (noun)
the activity of exerting your muscles in various ways to keep fit	bodybuilding by exercise that involves lifting weights
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)	weightlift (verb)
do physical exercise	lift weights
give a workout to
learn by repetition
put to use
carry out or practice; as of jobs and professions