Ace hit the nail on the head for the GTVA. Likely, the GTA prior to the node collapse was probably something very similar, an alliance of smaller nations that probably had their roots in Sol with their own colonies in the outer systems. Which means when the node collapsed, the colonies were all that remained of their original states and created the internal divisions that allowed the Hades rebellion to take what root it did. The GTVA reaffirmed the old GTA alliance, and added the Vasudans on for good measure.
As a point of issue, the war between the Terrans and Vasudans should be called the 14 Year War officially, as it may not necessarily be the only Terran-Vasudan war. On the other hand, the odds of another 14 year war are pretty remote, especially with beam cannons.