If you are working in a multi-client environment, it is recommended to assign all permissions using Outlook on the Web. The terms and levels one can choose from to assign to others are not consistent between Outlook on the Web and Outlook.
You do have the option to grant the 'Editor' the ability to view (full details) Private events. By default, 'Editor' cannot view/modify events set to Private. In addition a 'Editor' (delegate) can also be selected to receive calendar notifications/requests/invitations. Editor Provides Assignee with 'Delegate' access. Author Provides Assignee with 'limited details' access. Reviewer Provides Assignee 'Full' detail read access.
Important: Office 365 team recommends using the delegate access feature to set permission levels above 'read'. If you are looking to grant someone 'read' permissions only, use the following doc: Oulook - assign 'read' permissions to your calendar. Important: This document covers 'read/write/modify' permission levels only. People outside your organization will be sent a URL that they can use to view your calendar. When you grant permissions to your calendar with someone inside your organization (UWM), they will be able to add it directly to their calendar view in Outlook or Outlook on the Web. You can use Outlook to assign 'read/write/modify' permissions to your calendar.