With the creation of the City of New York, the municipal limits were extended to take in more of Westchester County, as well as Queens County (including the incorporated Long Island City), the incorporated city of Brooklyn and the entirety of Richmond County (a.k.a. Staten Island).
Five "boroughs" were created; Manhattan, The Bronx, Queens, Brooklyn and Richmond. Manhattan and the Bronx formed New York County. Queens comprised Queens County, Brooklyn was conterminous with Kings County and Richmond with Richmond County.
Three eastern towns in Queens-Queens County were incorporated out of the boundaries of the City of New York in 1899. They became Nassau County. In 1914, the borough of The Bronx became Bronx County. Richmond was renamed as the Borough of Staten Island in 1975 (but was still the jurisdiction of Richmond County).