How are to, do, fu, and ken different?

The difference is simply a matter of their historical backgrounds: they are all defined in the same manner under the local autonomy law.
To is used exclusively for Tokyo, as in Tokyo-to (Tokyo Prefecture, sometimes called Tokyo Metropolis), and do is used only for Hokkaido.
There are two prefectures with fu attached to them, which are Osaka-fu and Kvoto-fu, and there are 43 ken, usually translated as prefecture.