Publishing: this options allows you to publish a calendar for use on a web page, for a non-Office365 user to see, etc.
Sharing: this option allows you to specify who can view your calendar, the details they can see and if they have editing or delegate rights. Giving Permissions: this option allows you to specify who can view your calendar, the details they can see and if they have editing rights. NOTE: if you are trying to share a resource, see Office 365 Resource Management There are several options for sharing your personal calendar with other users - sharing, publishing, giving permissions.
