correctness vs quality

correctness and quality both are nouns.

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

As nouns, quality is a hypernym of correctness; that is, quality is a word with a broader meaning than correctness:

correctness (noun)	quality (noun)
conformity to fact or truth	an essential and distinguishing attribute of something or someone
the quality of conformity to social expectations	(music) the distinctive property of a complex sound (a voice or noise or musical sound)
	a degree or grade of excellence or worth
	a characteristic property that defines the apparent individual nature of something
	high social status

correctness (adjective)	quality (adjective)
	of superior grade
	of high social status