When doing box step-ups, step up and stop on top of the box fully extended. When doing box step-overs, step both feet on top of the box but you do not have to fully extend. Step-ups are more for strength and stepovers are more for conditioning.
You can use weights or kettlebells when doing both step-ups or step-overs. It is important that when using kettlebells, make sure to have a solid, tall torso.