Flatbush Gardener has taken NYShitty to task for her geography. But Heather has it right (even if she doesn’t know it).
Historically, the area from roughly Atlantic Avenue south to Red Hook (including current Carroll Gardens, Boerum Hill and Cobble Hill) were called “South Brooklyn”. This was back when Brooklyn Heights and downtown were just plain “Brooklyn”, and North Brooklyn (Williamsburg, Bushwick and Greenpoint) were the “Eastern District.” I’m not sure where Park Slope, Fort Greene, Clinton Hill and Bed-Stuy fit into all of this. But from 1855 to 1898, these areas were “Brooklyn”, and everything else was a separate township. And South Brooklyn continued to be called South Brooklyn through most of the 20th Century.