By definition, a true civil war is when two legitimate claimants to government attempt by force of violence to take control of an entire nation while crushing the opposition.
England had a civil war. So did Russia, Ireland and Spain. Technically, America never fought a civil war. The Confederate States of America never sought to conquer the North. They just wanted their independence, which was constitutionally correct at the time.
But for the sake of understanding the mainstream moniker, I’ll refer to The War When The North Invaded America simply as “The Civil War”.