Hello,
As I understand it, the main difference between Privateers and Pirates is their status. Privateers had a para-military status which allow them to act under the laws of war. They do basically the same actions as Pirates (and the Navy), such as robbing at sea, taking/pillaging settlements and killing peoples, but in war time and against enemy factions. For the Navy and the Privateers this is warfare, for civilians that are not under military status this is Piracy, Pillaging and Murder. Crimes currently allow to Pirates. I wanted to add that all pirates were not always being heavily hunted down, in some periods and areas they were at least tolerated if not encouraged, which add to the confusion. Sorry for my English.
Cheers