The South leaving the American Union is no different than the Colonists leaving the British Union. Neither was a civil war in which both combatants fought for control of the central government.
In both cases, one combatant fought for independence from the central government, while the other fought to subjugate those who would be free of control from the central government.
Again, as I explained before you jumped in, trying describing civil war in its most basic form without resorting to convenient historical events.