Generally, accounts will only be linked to one app. If your account is linked to multiple apps, however, you can choose which app your should content should be published to.
Public: Anyone can access
If you want everyone on your app to access a story/stream, then choose this option.
Choose "Public Story" / "Public Stream"
Public publishing is great if you have a public app (meaning that anyone can sign up without being invited).
It's also ideal if you have a preview or introduction story that you want everyone to see before you release group-specific stories.
Private: Group access only
If you have user groups, you will be able to choose which groups can access your story or stream.
This option is perfect if you have specific stories for specific groups.