vainglory vs vanity

vainglory and vanity both are nouns.

Word	Noun	Adjective	Verb	Adverb
vainglory	Yes	No	No	No
vanity	Yes	No	No	No

As nouns, vanity is a hypernym of vainglory; that is, vanity is a word with a broader meaning than vainglory:

Other hypernyms of vainglory include conceit, conceitedness.

vainglory (noun)	vanity (noun)
outspoken conceit	low table with mirror or mirrors where one sits while dressing or applying makeup
	the trait of being unduly vain and conceited; false pride
	the quality of being valueless or futile
	feelings of excessive pride