age bracket vs age group

age bracket and age group both are nouns.

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

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

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

Other synonyms of age bracket include cohort.

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