sterility vs barrenness

sterility and barrenness both are nouns.

Word	Noun	Adjective	Verb	Adverb
sterility	Yes	No	No	No
barrenness	Yes	No	No	No

As nouns, barrenness is a hyponym of sterility; that is, barrenness is a word with a more specific, narrower meaning than sterility:

sterility: the state of being unable to produce offspring; in a woman it is an inability to conceive; in a man it is an inability to impregnate
barrenness: the state (usually of a woman) of having no children or being unable to have children

Other hyponyms of sterility include impotence, impotency, cacogenesis, dysgenesis.

sterility (noun)	barrenness (noun)
the state of being unable to produce offspring; in a woman it is an inability to conceive; in a man it is an inability to impregnate	the quality of yielding nothing of value
(of non-living objects) the state of being free of pathogenic organisms	the state (usually of a woman) of having no children or being unable to have children