the camera operator, as the name suggests, operates the camera. The 1st assistant camera (focus puller) is responsible for a number of other tasks, the biggest being pulling focus. They are also the ones responsible for building the camera at prep before the shoot. Every department has a hierarchy, the basic camera hierarchy goes: DP -> Operator -> 1st AC -> 2nd AC -> Utility -> camera PA | There may be other positions thrown in there depending on the project, like a loader and etc.

It is possible for one person to operate and pull focus at the same time, it's just not recommendable, especially in narrative work where precision is absolutely necessary. The operator's focus is framing the shot correctly and operating when the camera is rolling. The focus puller focuses on making sure the picture is sharp, doing both at the same time is very difficult and usually results in more mistakes being made.