atrocity vs barbarity

atrocity and barbarity both are nouns.

Word	Noun	Adjective	Verb	Adverb
atrocity	Yes	No	No	No
barbarity	Yes	No	No	No

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

Other hyponyms of atrocity include barbarism, brutality, savagery, outrage, enormity.

As nouns, atrocity and barbarity are synonyms defined as:

atrocity and barbarity: the quality of being shockingly cruel and inhumane

Other synonyms of atrocity include atrociousness, barbarousness, heinousness.

atrocity (noun)	barbarity (noun)
an act of atrocious cruelty	a brutal barbarous savage act
the quality of being shockingly cruel and inhumane	the quality of being shockingly cruel and inhumane