There really is no difference; Your web root (where you upload your web site (web accessible) files to) is the public_html directory. The www directory is just a symbolic link (i.e., an aliased name that points to the same place) as public_html.

To upload/publish, you should use public_html, however, since some FTP and other publishing software can complain about a symbolic linked directory.

Important Note regarding symbolic links; they are simply another path to the same area, they are not copies (removing a file from one will remove the file from both locations!).