correctness vs rightness

correctness and rightness both are nouns.

Word	Noun	Adjective	Verb	Adverb
correctness	Yes	No	No	No
rightness	Yes	No	No	No

As nouns, correctness and rightness are synonyms defined as:

correctness (noun)	rightness (noun)
conformity to fact or truth	according with conscience or morality
the quality of conformity to social expectations	conformity to fact or truth
	appropriate conduct; doing the right thing
	conformity with some esthetic standard of correctness or propriety