“We had the War Between the States, the Civil War, between 1861 and 1865.”
What is frequently called the “Civil War” was not. A civil war is a war within a country.
Lincoln’s War was a war between two countries - the United States of America and the Confederate States of America.
All civil wars involve two political entities emerging from one.
They compete and battle with each other until one wins.
Thus it has always been.
Civil wars always involve territory held by each respective entity.
These entities can call themselves anything they want, including “country”.
It does not preclude the fact they were part of one political entity, and have broken away to form a new one.
A similar case can be made for the American Revolution as being a civil war.