air alert vs alarum

air alert and alarum both are nouns.

Word	Noun	Adjective	Verb	Adverb
air alert	Yes	No	No	No
alarum	Yes	No	No	No

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

air alert: the warning signal that begins a period of preparation for an enemy air attack
alarum: an automatic signal (usually a sound) warning of danger

Other hypernyms of air alert include alarm, alert, warning signal.

air alert (noun)	alarum (noun)
the warning signal that begins a period of preparation for an enemy air attack	an automatic signal (usually a sound) warning of danger
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