austerity vs self-denial

austerity and self-denial both are nouns.

Word	Noun	Adjective	Verb	Adverb
austerity	Yes	No	No	No
self-denial	Yes	No	No	No

As nouns, self-denial is a hypernym of austerity; that is, self-denial is a word with a broader meaning than austerity:

austerity: the trait of great self-denial (especially refraining from worldly pleasures)
self-denial: the trait of practicing self discipline

Other hypernyms of austerity include self-discipline.

austerity (noun)	self-denial (noun)
the trait of great self-denial (especially refraining from worldly pleasures)	the act of denying yourself; controlling your impulses
	renunciation of your own interests in favor of the interests of others
	the trait of practicing self discipline