rite vs vigil

rite and vigil both are nouns.

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

As nouns, vigil is a hyponym of rite; that is, vigil is a word with a more specific, narrower meaning than rite:

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

Other hyponyms of rite include watch, last rites, orgy, circumcision, liturgy, office.

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