age group vs age bracket

age group and age bracket both are nouns.

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

As nouns, age group and age bracket are synonyms defined as:

age group and age bracket: a group of people having approximately the same age

Other synonyms of age group include cohort.

age group (noun)	age bracket (noun)
a group of people having approximately the same age	a group of people having approximately the same age