age vs blue moon

age and blue moon both are nouns.

Word	Noun	Adjective	Verb	Adverb
age	Yes	No	Yes	No
blue moon	Yes	No	No	No

As nouns, blue moon is a hyponym of age; that is, blue moon is a word with a more specific, narrower meaning than age:

Other hyponyms of age include month of Sundays, aeon, eon, year dot.

age (noun)	blue moon (noun)
how long something has existed	a long time
a time of life (usually defined in years) at which some particular qualification or power arises
a late time of life
an era of history having some distinctive feature
a prolonged period of time