rightness vs morality

rightness and morality both are nouns.

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

As nouns, morality is a hypernym of rightness; that is, morality is a word with a broader meaning than rightness:

rightness: according with conscience or morality
morality: concern with the distinction between good and evil or right and wrong; right or good conduct

rightness (noun)	morality (noun)
according with conscience or morality	concern with the distinction between good and evil or right and wrong; right or good conduct
conformity to fact or truth	motivation based on ideas of right and wrong
appropriate conduct; doing the right thing
conformity with some esthetic standard of correctness or propriety