waking vs wakefulness

waking and wakefulness both are nouns.

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

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

waking: the state of remaining awake
wakefulness: a periodic state during which you are conscious and aware of the world

waking (noun)	wakefulness (noun)
the state of remaining awake	a periodic state during which you are conscious and aware of the world
	the process of paying close and continuous attention
	a temporary state in which you are unable (or unwilling) to sleep

waking (adjective)	wakefulness (adjective)
marked by full consciousness or alertness