rightness vs correctness

rightness and correctness both are nouns.

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

As nouns, rightness and correctness are synonyms defined as:

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