For the example of a right-handed shooter firing around a corner to their left, let's assume they are facing north, so they are firing to the west. In my mind's eye I picture it as the shooter keeping most of their body behind the corner, still facing north, and only leaning their torso and head out enough so that their right arm (holding the gun - which I see as being a handgun) is pointing west, to the left, and can make the shot. Their head is turned to the left (west) as well. So their target would see the gun just clearing the corner, along with the attacker's shoulder and head. (This is unlike your first photo above, where the shooter is using their left hand.)
For the example of the right-handed shooter firing around a corner to their right, they're now firing to the east. I picture this (again, using a handgun), as the shooter at the very least having to lean out their torso and head much further so their whole right arm can point to the right (to the east), and probably also expose some of their left leg for added stability. This is closer to your second photo, but I'm picturing the shooter as being a little less exposed than that.
Does that help?
I'm assuming a handgun here because Espionage! is spy-centered, and most spy characters would presumably be running around with handguns (because they're more concealable, etc.)