What is the difference between a "private" and "public" project?
The only difference between private and public projects is that a private project is not listed anywhere on the site. Unless you give the project address to someone they will not be able to find it (unless they guess the address which is highly unlikely). The idea behind "private" projects is that if you were to say create a plugin but only want it available to a select group of people. You could then link to the project from your website letting your specific group know where to find it.