(おしおき) To punish.   KIDS
する(ばつする) To punish. The difference - You use 罰 when someone has broken an established rule. This is anything from the legal system to high school rules like ‘don’t run in the halls.’
お仕置き is used more like with little kids (or with s/m slaves, for that matter). there doesn’t have to be a rule – just a sense that someone did something bad. It’s more like ‘sit in your room and think about what you did.’