If you see them on the panel, then they MUST show on the Buttons tab. If you have lots of buttons, take into account that by default there is pagination when reaching 150 buttons, perhaps you are missing the previos/next page links for pagination. You can edit /var/www/html/fop2/admin/config.php and increase buttons_per_page to a higher number if you want to avoid pagination.
If you do not have lots of buttons, then you might have some manual configurations or buttons.cfg files? I cannot say as it is your configuration, you should inspect /usr/local/fop2/fop2.cfg and see if its specifying any particular buttonfile=xxx or grep that directory for some of those buttons that you see on the panel but not on the manager.