In the first case it's a part of a place name. A good example of this is "South Korea". In the second case "the south side" is not a part of the place name of "Baltimore".
Don't capitalize names of directions like north, south, east, and west when used to refer to direction and location, but do capitalize these words when they appear in the names of places and regions.
If you Google it, you'll see that the Wikipedia article states that:
South Baltimore is a neighborhood in the Southern District of Baltimore, located to the west of the neighborhood of Riverside and south of Federal Hill.
So in the same way that "South Korea" is a nation, "South Baltimore" is a neighborhood, and it's therefore capitalized as the word "south" just happens to be a part of the name.