awake vs wake up

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

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

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

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

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

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