Rex Brynen
I would largely agree (although I would probably count RSA as a civil war), in general civil wars are a subset of insurgencies. A few defining features:

1) Severity. We don't consider the Red Army Faction versus West Germany a civil war. (I'm sometimes tempted to define civil war as an insurgency that reaches the point that the government thinks "holy crap, we could lose this!")

2) Internal actors (although they may have external patrons). Violence wholly directed at an occupying power would not be a civil war.

3) Insurgency targets an established authority. In those rare cases where there is no authority--Somalia at certain times--you could have the unusual case of a civil war that isn't an insurgency.

Rex, what would be DRC?
A war conducted by local actors in the name of external powers who are not happy that the pupet they pupet in place, after overpassing an established authority, is no more listening to them?
Just to add some fun, you can even add the fact that you have at least 2 external powers who are fighting indirectly to take control over strategic natural resources in a cold war like manner... (But that's just if you wanna go in details).

By the way, Liberia was no insurgency. It was a civil war but the rebel (Taylor) invaded the country without national support and insurgent network.
But 1) his troops were mainly liberian and 2) his obective was to reconquere power in the name of a liberia ethnic group (the Kongo).