barbell vs free weight

barbell and free weight both are nouns.

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

As nouns, free weight is a hypernym of barbell; that is, free weight is a word with a broader meaning than barbell:

barbell: a bar to which heavy discs are attached at each end; used in weightlifting
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

Other hypernyms of barbell include exercising weight, weight.

barbell (noun)	free weight (noun)
a bar to which heavy discs are attached at each end; used in weightlifting	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