Most of the side levers are side opener. For a very short time at the beginning of hammerless development, there were side levers that not only opened the gun, but also cocked it. I have a Lancaster side cocker (right side) and have had a number of Lefever side cockers. On the Lancaster the side lever both opens and cocks the gun. On Lefever, there is a thumb push opener and a separate (left side on all I have seen) side cocker.

Rich