The difference requires that you actually believe that supernatural will punish you and your family if you break that oath. Which has also other consequences - like your family being motivated to be very controlling over what they allow you to say or do in the fear it will have consequences on them.

Other consequence is assumption that if bad things (sickness, injury, fire, ...) happen, it is punishment for what X had done or not done. This leads to revenge toward other humans for unrelated sicknesses, injuries, fires, ... .