normality vs conformity

normality and conformity both are nouns.

Word	Noun	Adjective	Verb	Adverb
normality	Yes	No	No	No
conformity	Yes	No	No	No

As nouns, conformity is a hypernym of normality; that is, conformity is a word with a broader meaning than normality:

Other hypernyms of normality include conformance.

normality (noun)	conformity (noun)
expectedness as a consequence of being usual or regular or common	acting according to certain accepted standards
conformity with the norm	hardened conventionality
(of a solution) concentration expressed in gram equivalents of solute per liter	correspondence in form or appearance
being within certain limits that define the range of normal functioning	orthodoxy in thoughts and belief
	concurrence of opinion