wakefulness vs waking

wakefulness and waking both are nouns.

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

As nouns, waking is a hypernym of wakefulness; that is, waking is a word with a broader meaning than wakefulness:

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

Other hypernyms of wakefulness include physical condition, physiological condition, physiological state.

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

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