Triggered and activated abilities can be divided into two parts: condition, and effect. For activated abilities, the condition is a specific cost being paid and is separated from the effect by a colon, while triggered abilities just happen whenever a specified criteria is met. When copying one of these abilities, you only ever copy the effect, not the condition.
So if you copy an ability that says "whenever x happens, do y" you get y effect twice without having to meet the x condition a second time. If you copy an ability that says "do x: get y effect" you get y effect without having to do x a second time.
Hope that makes sense!