vigil vs rite

vigil and rite both are nouns.

Word	Noun	Adjective	Verb	Adverb
vigil	Yes	No	No	No
rite	Yes	No	No	No

As nouns, rite is a hypernym of vigil; that is, rite is a word with a broader meaning than vigil:

vigil: the rite of staying awake for devotional purposes (especially on the eve of a religious festival)
rite: an established ceremony prescribed by a religion

Other hypernyms of vigil include religious rite.

vigil (noun)	rite (noun)
a purposeful surveillance to guard or observe	any customary observance or practice
the rite of staying awake for devotional purposes (especially on the eve of a religious festival)	an established ceremony prescribed by a religion
a period of sleeplessness