Washington, DC, is many different towns, which sounds trite, but the most important aspect of that concept is that people outside of the District metropolitan area do not recognize DC as anything more than a symbol of the federal government.
In this world view, homes and neighborhoods don't really exist in DC. The District government is a joke, side show acts, like The Players in Hamlet, or maybe like the mock government some people played at in high school. People in DC work for the government, lobby the government, contract with the government, or don't work at all.
In part, it's not a terribly wrong impression, since DC so often becomes the plaything of itinerant powergrubbers who are completely unanswerable to the subjects on whom they conduct their experiments. However, it certainly passes over the lives of most residents of DC, who don't spend much of their time thinking about the federal government, or politics for that matter, except in the sense that everyone else in the US thinks about those things. Sure, it rankles to have no representation in Congress when you have a complaint or an issue, but it's not the sort of thing that creeps into your daily conscious state as you're trying to catch the L2 so you can hit the Safeway for groceries before it gets too late.
I should be thinking more about this bifurcated urban identity. The city as lived experience and the city as imagined space, in particular as tourist destination. London, New York, and Paris may be tourist destinations as well, but people talk about the experience of the cities. I don't know if people visiting DC think about it as a city so much as they think of it as a collection of monuments and museums.