Productive supports two types of projects: public projects and private projects. When you're creating a new project, the you'll be asked which type your new project should be.
The main difference is that on public projects, all your team members can collaborate, while private projects require an invitation from the project manager.
You can also convert projects from private to public and vice versa. Have in mind that once a public project has been converted into a private one, all new members will have to be added by the project manager. Also, converting private projects into public ones will make its data accessible to the whole team.
To convert, go to the project in question and click on Options > Edit project.
Again, you'll see the first screen where you can set the project as public or private: