I nsurgency differs from terrorism in that civil violence within a single country is involved whereas with terrorism, there's usually cross-national violence. Insurgency is a word meaning armed revolt. Insurgency involves civil gang or mob violence, and is rarely organized. Therefore, waging war against it cannot be systematic.
Humanitarian relief is put in place whenever it's safe to do so.
It's important to distinguish counter-insurgency operations from warfare. If you use strong-arm military tactics, you run the risk of uniting all the different groups, and then you've got a guerilla war on your hands. If you act too slowly or softly, a chain reaction takes place, and you've got countless acts of mob violence on your hands. You can also let the civil violence run its course. There's actually a school of thought that supports this idea.