birth rate vs fertility rate

birth rate and fertility rate both are nouns.

Word	Noun	Adjective	Verb	Adverb
birth rate	Yes	No	No	No
fertility rate	Yes	No	No	No

As nouns, birth rate and fertility rate are synonyms defined as:

birth rate and fertility rate: the ratio of live births in an area to the population of that area; expressed per 1000 population per year

Other synonyms of birth rate include birthrate, fertility, natality.

birth rate (noun)	fertility rate (noun)
the ratio of live births in an area to the population of that area; expressed per 1000 population per year	the ratio of live births in an area to the population of that area; expressed per 1000 population per year