air base vs base of operations

air base and base of operations both are nouns.

Word	Noun	Adjective	Verb	Adverb
air base	Yes	No	No	No
base of operations	Yes	No	No	No

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

air base: a base for military aircraft
base of operations: installation from which a military force initiates operations

Other hypernyms of air base include base.

air base (noun)	base of operations (noun)
a base for military aircraft	installation from which a military force initiates operations