The Federation are a breakaway faction from the Unitary Republic of "Terra" - Terra meaning Earth. Meaning they revolted against the Earth Government which is the center of the Republic. I realize I may have been clearer with this fact, but I did reinforce this idea in the additional information about them. Sorry again for the confusion.

The Federation's full name is The Free Citizen's Federation - free from the apparent dictatorial nature of the republic and gives more power to the citizens under a Federal government i.e. Free Citizen's Federation. I know it's very imaginative.