Technically not a civil war. Carefully and properly used, a civil war is a word for a war to overthrow a government; for instance, the English Civil War is, in fact, a civil war.
The US "civil war" isn't. It's a war of independence.
Here is the defintion from globalsecurity.org:
civil war: A war between factions of the same country; there are five criteria for international recognition of this status: the contestants must control territory, have a functioning government, enjoy some foreign recognition, have identifiable regular armed forces, and engage in major military operations.
Sounds to me, according to there defintion, it was a Civil War.