Public Software was coined by Dan Nachbar, the founder of the Public Software Institute. http://www.public-software.com/
The concept based is upon the key phrase "Publish or Pay" which means, if you make any derivatives of public software you must publish the source code or you must pay an appropriate contribution to the public software industry. Use of the software, is, of course, free.
Where as Free Software guarantees equal access to both the binary and source code, Public Software extends this definition with the distinct ability to customize or include the software in a proprietary solution that meets corporate needs without being forced to publish the source code if an appropriate contribution is made and due credit is given.
The Public Software License ("PSL") is available at http://www.public-software.com/licensing/