I think I've called them the Federal Army here and sometimes Union but Federal just, at least to me, seems more specific to following orders from the United States government and sure doesn't fit into Confederate States forces. Like when a courthouse says "Federal" on the front you know it's not gonna be hearing property line disputes or a jaywalking case.
Maybe it is a bit like Cowboys and Indians, or is it Cavalry and Native Americans? Hmm, gotta think on that a bit.
Pam