To me, it’s a bit confusing. I was born in Brooklyn, which is a borough of New York City. However I was also born in Kings County, a county of New York State.

The borough of Brooklyn has the same border as the county of Kings, which pretty well makes them equivalent.

Lastly, people born in the borough of Manhattan (county of New York), normally say they were born in New York City (not Manhattan), yet people born in the other 4 boroughs (Brooklyn, Queens, Bronx, Staten Island) usually name their borough, not New York City.

Just thought it interesting.