wake up vs awake

wake up is not an adjective while awake is an adjective.

Word	Noun	Adjective	Verb	Adverb
wake up	No	No	Yes	No
awake	No	Yes	Yes	No

As verbs, wake up and awake are synonyms defined as:

Other synonyms of wake up include arouse, awaken, come alive, wake, waken.

wake up (adjective)	awake (adjective)
	not in a state of sleep; completely conscious
	mentally perceptive and responsive

wake up (verb)	awake (verb)
stop sleeping	stop sleeping
cause to become awake or conscious