Well, That's actually a great question. Thank you for asking.
Short and sweet, it wasn't. Before 1783, America was a part of the great British Empire, though America as we know it today was only the infant version of the giant it would grow up to be. Many people took direct leadership from their governors, who acted as the voice of the English Crown and Parliament. They followed English Laws and English Taxes, as well. When the War for Independence started, the Patriots had two goals:
Overthrow the English Rule in America
Establish a new system of Government where the former colonies would act in a relationship of mutual friendship away from a strong national government.
The Agreed-upon definition of a Civil War is a war fought between the people of the same country. Even though, many of the people in the North American Colonies were technically English citizens, many of them were born on the North American Continent and had never laid eyes upon England. The North American Colonies were not their own separate country, but at the same time, they were not a part of England. Instead, they were under direct control of England. So it's considered a Revolution, as it was the Forceful overthrow of a current Government. Revolutions tend to be part of a Civil War, but whenever a Colony rebels from its mother country, it is typically described as a War for Independence or Revolution.
Once again, excellent question. Hope this helps.
If you want me to clarify a bit, I'd be happy to.