All areas of New York State have County names, but New York City also has Borough (Boro) names for its five Counties. Two of the Borough names are the same as the County names and three are different. Virtually everybody uses the Borough names. The County names are just used for legal and government purposes. Below I have listed the names of the five Boroughs, together with their County names for easy reference.
Borough Name--------County Name
Manhattan----------------New York
Brooklyn-------------------Kings
Staten Island-------------Richmond
The Bronx------------------Bronx
Queens--------------------Queens
The five burroughs of New York City are Manhattan, the Bronx, Brooklyn, Queens and Staten Island. Each one is its own county. Manhattan is Manhattan County, Bronx is Bronx County, Queens is Queens County, Brooklyn is Kings County and Staten Island is Richmond County. Brooklyn and Queens are both on Long Island and are 2 of the 4 counties that make up Long Island. (Nassua and Suffolk being the other 2 on the eastern side, Brooklyn and Queens are both West Long Island). Northwest of Brooklyn and Queens in Manhattan, which is often referred to as the city. Harlem is a part of Manhattan but is not a burrough, it is a neighborhood. North of Manhattan is the Bronx. And then the least populated Burrough, southwest of Manhattan, West of Brooklyn and Queens is Staten Island. Staten Island and Manhattan are both their own islands. The Bronx is the only burrough on mainland New York.