Having studied state militia organizations (ca 1860) for thirty years, I will offer that evidence is abundant. However, it's off the beaten path of Civil War studies, so no one ever discusses this topic.
There is no point in pursuing this argument. Saying there's no difference between state militia and Confederate military organizations is like saying there's no difference between a rifled musket and a smoothbore. All the evidence in the world would fail to make a dent.