This is a link to a lesson plan i found that teaches students what is safe to post online. It makes the difference between private and public information clear.

The learning objectives are:

• Identify the reasons why people share information about themselves online.
• Explain the difference between private and personal information.
• Explain why it is risky to share private information online.

https://www.commonsense.org/education/digital-citizenship/lesson/private-and-personal-information