Short answer: When there are synchronisation issues, it could either be (1) a server/login issue, (2) a visibility issue, or (3) the items in question are not where you think they are
Server/login issue
On the device where an item doesn't appear, it could be due to the fact that the device can't reach the server.
Either the server is down or the "client" is not authenticated anymore.
To check whether Apple's servers are down, just visit https://www.apple.com/support/systemstatus/
For other services, I recommend Downdetector: https://downdetector.com
If it's an authentication issue, the best is to visit "Settings" then "Contacts" or "Calendar" then "Accounts" and check if you need to enter a password somewhere.
Visibility issue
With contacts and calendars, it's possible to have multiple of them (i.e. Work, Personal, Family) for each separate account (i.e iCloud, Google, Yahoo, ...)
Assuming that both devices are connected to all your accounts properly, then you might have hidden one or more Contacts groups or one or more calendars, differently on your devices.
With contacts, for instance, you need to open the app on both devices, then tap on "Groups" (top left corner) and check if you have the same groups visible on both devices.
For the Calendar app, you need to tap on "Calendars" at the bottom.
Items in different locations
The default location to store items could be different on different devices.
For instance, on an iPhone, new contacts could be saved by default in iCloud whereas on an iPad they're saved in Google Contacts.
If both services (iCloud and Google) are properly configured on both devices, then all contacts should appear on both devices regardless of the default save location.
But if one service is not configured on one device (let's say Google on the iPhone), then a contact saved on the iPad (and synchronised with Google's servers) will not appear on the iPhone.
In that case, on both devices, you should visit "Settings" then "Contacts" and "Calendar" then check what is the default account and make sure that all the required accounts are set up properly.
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