This is a good topic and a good point.
I've heard the "Second Great War" and have used that, but you're right, I probably just heard that from fan sites.
So what is it called? "The War of 2367"? "The Second Shivan Invasion?"
One thing is I guess it depends on how you think about it, like if it should be called two things.
If you consider it from the GTVA vs. the NTF, the it could be called something like "The NTF Rebellion" or "The Neo-Terran War".
But for the Shivan side of the war, you have to consider it from the GTVA's point of view. They didn't think that maybe the Shivans had another purpose other than us. That they could have just invaded us with that juggernaught fleet years ago. To the GTVA, the Shivans attacked us first and so we had to fight back their second invasion (not knowing that their only goal was Capella). So from the GTVA's it could be called "The Second Shivan War" or "The Second Shivan Invasion".
So, what do we call each?
Joe.
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