Why distinguish common goods from public goods?

The main reason to distinguish between common and public goods is to determine who will manage the goods. In common goods, usually there is some sort of government oversight. In public goods, the public at large is in charge of monitoring and protecting the goods.

A public good is a good that is non-excludable and non-rivalrous and a common good is non-excludable but rivalrous at times. A public good is a good where everyone is able to use the service/good and one person won't trump another for it. A public good example is air, everyone is able to breathe in the air and use it and one person will not be allotted more than the next. An example of a common good is a public school. A public school is open for everyone to use but not everyone will be able to use it at the same time, if spots are limited.