What are the capabilities that a super-administrator has that an administrator does not have?
The codex page on user capabilities does not have a list of capabilities of the super-admin. It lists only the capabilities of the administrator.
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The super_admin has access to all admininstrator APIs and also the multi-site functions. If you go to the codex page, it will say so: http://codex.wordpress.org/Roles_and_Capabilities#Capability_vs._Role_Table
You can find the multisite functions here: http://codex.wordpress.org/Function_Reference#Multisite_functions
If you want to do a more fine-grain investigation of what it can call, I suggest you get familiar with the WP code. The funtion you should grep for is_super_admin
Hope this helps.
The super admin owns the installation and can do absolutely everything. The admin owns the actual site (or rather, blog...).
The two are the same on single site installs. On multisite installs, the admin cannot do a couple of things that relate to the filesystem, e.g. install/upgrade/delete themes and plugins, to site management, e.g. view all sites or change site options, and to user management, e.g. he can add and remove existing users to his sites but not create or delete them...
" I'd like to know which capabilities (like edit_posts, delete_posts) does the super_admin has the admin doesn't have. "
Install plugins & themes, upgrade the site. Admins in a network can't do this.
I swear the codex has this listed somewhere...
Programmatically, if you're looking to check for this, just use an if is_super_admin, not a has_cap.