The South Bronx is essentially at northern end of Manhattan and the Harlem vicinity. It’s also the home to Yankee Stadium. The remainder of the Bronx is simply “the Bronx” as far as I’m concerned. Lived in the south-east area for a short while.
I used to drive the Cross Bronx Expressway in the 60s and 70s.
Looked more than a bit run-down.