badness vs foulness

badness and foulness both are nouns.

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

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

Other hyponyms of badness include raininess, distressfulness, seriousness.

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