wakefulness vs vigil

wakefulness and vigil both are nouns.

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

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

wakefulness: a periodic state during which you are conscious and aware of the world
vigil: a period of sleeplessness

Other hyponyms of wakefulness include arousal.

wakefulness (noun)	vigil (noun)
a periodic state during which you are conscious and aware of the world	a purposeful surveillance to guard or observe
the process of paying close and continuous attention	the rite of staying awake for devotional purposes (especially on the eve of a religious festival)
a temporary state in which you are unable (or unwilling) to sleep	a period of sleeplessness