age group vs aged

age group and aged both are nouns.

Word	Noun	Adjective	Verb	Adverb
age group	Yes	No	No	No
aged	Yes	Yes	No	No

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

Other hyponyms of age group include elderly, young, youth.

age group (noun)	aged (noun)
a group of people having approximately the same age	people who are old collectively

age group (adjective)	aged (adjective)
	(used of tobacco) aging as a preservative process
	of wines, fruit, cheeses; having reached a desired or final condition; (`aged' pronounced as one syllable)
	at an advanced stage of erosion (pronounced as one syllable)
	advanced in years; (`aged' is pronounced as two syllables)
	having attained a specific age; (`aged' is pronounced as one syllable)