"Fertility rate" and "birth rate" are related, but used to mean different things. Observe that the first thing wikipedia says in the entries for both topics is

"Fertility rate" and "birth rate" are related, but used to mean different things. Observe that the first thing wikipedia says in the entries for both topics is, "Not to be confused with" the other. https://en.wikipedia.org/wiki/Total_fertility_rate https://en.wikipedia.org/wiki/Total_fertility_rate https://en.wikipedia.org/wiki/Birth_rate https://en.wikipedia.org/wiki/Birth_rate