free weight vs barbell

free weight and barbell both are nouns.

Word	Noun	Adjective	Verb	Adverb
free weight	Yes	No	No	No
barbell	Yes	No	No	No

As nouns, barbell is a hyponym of free weight; that is, barbell is a word with a more specific, narrower meaning than free weight:

free weight: sports equipment used in calisthenic exercises and weightlifting; it is not attached to anything and is raised and lowered by use of the hands and arms
barbell: a bar to which heavy discs are attached at each end; used in weightlifting

Other hyponyms of free weight include dumbbell.

free weight (noun)	barbell (noun)
sports equipment used in calisthenic exercises and weightlifting; it is not attached to anything and is raised and lowered by use of the hands and arms	a bar to which heavy discs are attached at each end; used in weightlifting