Punishment and Consequences

Is there a difference between punishment and consequences? 

Before this semester I never really thought there was. But now I understand that consequence is the result of the action and a punishment is what you choose to do. 

So how do we punish our children? I asked my mom about how she would punish us and she said she usually just let the natural consequences happen. 

So then the question came up how will I punish my children and I think my mom was really smart when she just let the natural consequences happen. With every action there is a consequence and I think the best way for me and my family is to just see what happens.