@George,
Well, the expression 'civil war' usually refers to a war between mainly civilians or an insurrection of civilians against the forces of the established government. Thus, the Russian revolution of 1917 was followed by a civil war between the Bolsheviks (Communist followers of Leninn) and the Mensheviks (followers of Kerenski). The Spanish Civil War in the 1930s came about when a group of insurgent high-ranking Spanish Army officers, led by Francisco Franco, pulled a coup d'etat and usurped control of the Republican government. The backlash they had to face was a phalanx of civilians, most of them very Left-wing, who rose up to defend what they called 'the Republic.
The war in North America was, in the final analysis, a formal war between two organized armies, uniformed and trained to wage war. Whether the Confederate States of America was or was not a "legitimate" government is immaterial in face of the fact that it was a
real, functioning governemnt. But 'American Civil War' is the most common designation for this conflict in the history books so we continue to use it. (IMO, 'war between the States' is no better because it ignores the Federalistic character of the war; this wasn't a warbetween individual states but between two central governments, the USA and the CSA).