Nomenclature:
Simple trigger...as the name implies
Single set trigger: a single trigger which must be 'set' by pressing forward to cock it. May or may not fire the gun set and unset. May or may not need to be set to cock the lock.
Double set - single acting trigger: a pair of triggers- a setting trigger (forward usually) and a hammer trigger (rearmost usually) which must be set to fire the gun. May or may not need to be set to cock the gun.
Double set - double acting triggers: a pair of triggers like the double set, single acting triggers, except the front trigger may also be used to trip the sear, firing the lock. May or may not need to be set before cocking the lock.
Here are some images of a single set trigger sold through MBS that can be used set or unset, and which allows the lock to be cocked without setting the triggers. I installed it in my Chambers' (Mark Silver) Virginia rifle...wonderful combination. The pictures show the trigger both set, and unset.
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