austerity vs self-discipline

austerity and self-discipline both are nouns.

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

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

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

Other hypernyms of austerity include self-denial.

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