Can someone please tell me what the difference is between the TentativePendingApproval and AddNewRequestsTentatively parameters of the Set-MailboxCalendarSettings cmdlet? They both appear to do the same thing.

I haven't found any actual scenarios in which either of these makes any difference. My reading is that TentativePendingApproval should control whether the room sends a "Tentative" response in a manual-approval situation (i.e. the request is out of policy, e.g. a conflict, and the user is a member of RequestOutOfPolicy), but after some testing, it appears thata Tentative is sent in this situation regardless of whether TentativePendingApproval is true or false. Ah well.

After more than a year of constant, rigourous, exhausingresearch... I have the answer! AddNewRequestsTentatively applies only to mailboxes that have the Calendar Attendant feature enabled (mailboxes that have AutomateProcessing set to 'AutoUpdate'). This option causes newly-received meeting requests to appear on the recipient's calendar as Tentative. However, no message is sent to the meeting organizer to indicate that the recipient accepted the meeting. TentativePendingApproval applies only to mailboxes that have the Resource Booking feature enabled (mailboxes that have AutomateProcessing set to 'AutoAccept'). This option is only relevant if the resource has received a meeting requestthat needs to be approved by a delegate of the resource. Under such circumstances, if TentativePendingApproval is set to 'true', then the meetingwill be accepted tentatively by the Resource Booking Agent. The meeting organizer will receive a message from the resource indicating Tentative acceptance, and the message will state, "Your request was received and is pending approval.".