Hi MwatersEMS,
Welcome to the Apple Community.
Re: Calendar on Mac Desktop vs iPhone
Seems iPhone methods, and Mac methods, are sometimes a little (or a lot) different from each other in use.
Generally, in many apps one can do a whole lot more on a Mac than on an iPhone, if you know how..
However, apologies if you already know the below methods, and find they are just not working on your Mac
In that case, you might want to chat online / talk with / Contact -Apple Support.
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Re: getting "none of the ones shared with me"
Apple Support's article:
(NB: is for Monterey, or open linked article to choose earlier Mac OS versions at the top, for accurate info.)
Share calendar accounts on Mac – Apple Support
says:
"See calendar accounts you have access to
- In the Calendar app on your Mac, choose Calendar > Preferences, then click Accounts.
- Select the calendar account, then click Delegation.
- A CalDAV account appears in the “Accounts I can access” list.
- For an Exchange account, click Add button , then enter the username of the person who gave you access.
- To see a delegated account’s calendars in the main Calendar window, select Show.
- To see a delegated account’s calendars in a new window, choose Window > [account name]."
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Re: creating new events: "they don't always sync with exchange"
Refresh calendars on Mac – Apple Support
says:
Refresh calendars on Mac
If you publish or share calendars, you may want to refresh them so that others can see your latest changes.
Or, if you subscribe to calendars, you may want to check for updates periodically to be sure you have the latest information.
A published or shared calendar has a Share Calendar button next to its name.
A calendar you subscribe to has a Subscription button next to its name.
- In the Calendar app on your Mac, choose View > Refresh Calendars.
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More info: Import or export calendars on Mac – Apple Support
Calendar User Guide for Mac – Apple Support
All the best :-)