The only real difference is that only an owner can add and remove other owners, as well as promote administrators to owners.
Think of an owner as a super-administrator. The person who originally creates the organization’s page automatically becomes an owner, but an organization can have multiple owners. Owners and administrators both have all permissions, including posting listings, editing the organization’s profile, and managing the permissions of other administrators, but an owner has control over other owners as well as administrators.
To promote an administrator to an owner, go to your organization's Dashboard and select Manage Administrators from the menu on the left side of the screen.
From this page, find the name of the person you would like to promote, select "Make owner" and you should be all set!