I have a theory that Springfield is a town in the 51st state, which is also called Springfield.
My biggest piece of evidence is in season 5, episode 8. Bart and Milhouse sing a parody of New York, New York, entitled "Springfield, Springfield".
That explains why it doesn't match up to any real state. It's not. Springfield is its own state, which has a town named Springfield in it. Its governor is Mary Bailey, and the capital is Capital City.