To state that the U.S. has 50 states is absolutely correct. To state that the U.S. has 50 states and one federal district is also correct. There are also many territories and possessions. So, it just depends on what you are talking about at the moment. See site below for a really good discussion of all the political divisions of the U.S.
D.C. was made as a district when the country only consisted of 13 states. It was strategically placed in middle ground (between Virginia and Maryland) on purpose. And to be fair the founding fathers of our country purposely put D.C. in a territory of it s own so no one state could regulate it.
They say America has 50 States precisely because it does, in fact, have 50 States.
we also have commonweaths..like puerto rico
D.C. isn t a state