This may be simplistic of me, but I always thought of a Civil War as an insurgency that has formed a psuedo-government, controls some territory, attempts to rule its territory in some sort of lawful fashion, and fields a conventional-type army with an established rank structure and some sort of control over their combatants. An insurgency would be like a "pre-civil war" phase of conflict in which there are people who are trying to overthrow the government in their neck of the woods. Additionally, an insurgency that wants to overthrow the government and establish control in the whole of a country would not, in my opinion, be a civil war. Note the word "civil" in the term "Civil War".
