awake vs alert

awake is not a noun while alert is a noun.

Word	Noun	Adjective	Verb	Adverb
awake	No	Yes	Yes	No
alert	Yes	Yes	Yes	No

As adjectives, awake and alert are synonyms defined as:

Other synonyms of awake include alive.

awake (noun)	alert (noun)
	a warning serves to make you more alert to danger
	an automatic signal (usually a sound) warning of danger
	condition of heightened watchfulness or preparation for action

awake (adjective)	alert (adjective)
not in a state of sleep; completely conscious	engaged in or accustomed to close observation
mentally perceptive and responsive	mentally perceptive and responsive
	quick and energetic

awake (verb)	alert (verb)
stop sleeping	warn or arouse to a sense of danger or call to a state of preparedness