foulness vs badness

foulness and badness both are nouns.

Word	Noun	Adjective	Verb	Adverb
foulness	Yes	No	No	No
badness	Yes	No	No	No

As nouns, badness is a hypernym of foulness; that is, badness is a word with a broader meaning than foulness:

Other hypernyms of foulness include severeness, severity.

foulness (noun)	badness (noun)
the attribute of having a strong offensive smell	that which is below standard or expectations as of ethics or decency
(of weather) the badness of the weather	used of the degree of something undesirable e.g. pain or weather
a state characterized by foul or disgusting dirt and refuse	an attribute of mischievous children
disgusting wickedness and immorality