Beta/Restricted: This is where I’d release new versions of my game first and have it restricted to a beta set of invited players only. The beta players can test the game version to find issues and provide feedback. It would be free.
My understanding is that the rule is mostly to avoid people flooding the search with copies of the same project. Your case seems to be that one project will be public, and one will be private.
I don’t think that will be an issue.