Depends on the photographer - when I filmed, I'd shoot so many still shots, then some video, then some still shots, then some ... and alternate like that. Others shoot the photos and then restart and do the video. Sometimes you can manage to do both at the same time - and one or two of the photographers may have an assistant.

We don't take stills from the videos and use them for photos, you'd see a huge drop in quality from what you see if we practiced that.