How can a war be civil? Good question, because civil means courteous, and is not very courteous to try to kill another person before they can kill you! By definition though, a Civil War is is struggle between "fellow citizens", as in The English Civil War (1642-1651).
Our "Civil War" is one of several names used for the bloodshed that occurred in the Eastern and Southern United States from 1861-1865. We Southerners call it "The War Between the States" because that's what it was. It was not "the Civil War" because it was not an internal conflict. It was a war between one country (the United States of America) and another country (the Confederate States of America).
Northern writers refer to it as a civil war because they did note recognize that the South had the right to secede.They, of course were dead wrong. Jefferson Davis was never brought to trial because it was feared that it would have been proven that the South had the right by the Constitution to secede.
Some call it Mr. Lincoln's War. I think it best summed up by those immortal words: "The War of Northern Aggression"! What do you think?