To be picky...Manhattan, Queens, and Brooklyn (and the Bronx and Staten Island) are boroughs, a division of the city that is AFAIK unique to NYC. Each borough is its own state county and has elected officials.
Neighborhoods are within the boroughs. Their boundaries are more fluid since they're not official administrative units in the same way. Harlem and Hell's Kitchen are neighborhoods in Manhattan; Crown Heights and Williamsburg are neighborhoods in Brooklyn, etc.
When Matt and Fisk talk about cleaning up their city via Hell's Kitchen, I see it as them taking ownership of the bit of Manhattan that they think they can control. Maybe Fisk hopes to spread out from there and Donald Trump his way through the 5 boroughs, but it'd take a whole army of vigilantes to patrol all of Manhattan, let alone all of NYC. For Matt, fixing his city just means doing what he can to fix his backyard. No one would ever refer to Hell's Kitchen as a city in and of itself.
Re: Where exactly is Hell's Kitchen?
Neighborhoods are within the boroughs. Their boundaries are more fluid since they're not official administrative units in the same way. Harlem and Hell's Kitchen are neighborhoods in Manhattan; Crown Heights and Williamsburg are neighborhoods in Brooklyn, etc.
When Matt and Fisk talk about cleaning up their city via Hell's Kitchen, I see it as them taking ownership of the bit of Manhattan that they think they can control. Maybe Fisk hopes to spread out from there and Donald Trump his way through the 5 boroughs, but it'd take a whole army of vigilantes to patrol all of Manhattan, let alone all of NYC. For Matt, fixing his city just means doing what he can to fix his backyard. No one would ever refer to Hell's Kitchen as a city in and of itself.