air alert vs qui vive

air alert and qui vive both are nouns.

Word	Noun	Adjective	Verb	Adverb
air alert	Yes	No	No	No
qui vive	Yes	No	No	No

As nouns, qui vive is a hypernym of air alert; that is, qui vive is a word with a broader meaning than air alert:

air alert: the condition in which combat aircraft are airborne and ready for an operation
qui vive: condition of heightened watchfulness or preparation for action

Other hypernyms of air alert include alert.

air alert (noun)	qui vive (noun)
the warning signal that begins a period of preparation for an enemy air attack	condition of heightened watchfulness or preparation for action
the condition in which combat aircraft are airborne and ready for an operation
the time period during which military and civilian agencies are prepared for an enemy air attack