I think your answer is in what you’ve said. The States were motivated by protecting slavery. The people who ran state governments were of a different class than private soldiers. They had different class interests. Hence, the distinction.

I don’t see many parallels between Vietnam and the Civil war other than both had soldiers whose interests were not the same as the elites who provoked and prosecuted the war.

But that’s the way it usually is. Nothing new. Soldiers are rarely responsible for starting or continuing wars. Most would just rather stay or go home.