As to triggers, there are single triggers that fire a rifle, and single set triggers(usually push forward to "set") that can fire, set or unset.I guess those could be called single set, double-throw triggers.

There are also double triggers where the rear trigger sets the front trigger to fire the gun, but just pulling the front trigger will not fire the rifle. That is a double set, single throw trigger.

Then there are the double set, double throw triggers, were pulling the front trigger without setting the rear trigger will fire the gun, or it can be fired by setting the rear trigger. Those are the triggers usually found on Mausers and many double triggered, US muzzleloading and ctg. rifles of the BP era.