I can see message content on my iPhone, but not on my Mac. What's up?

Are you referring to the Messages app?

Forward SMS/MMS text messages from your iPhone to your Mac or iPad - Apple Support describes what you need to do to forward text messages from your iPhone to your Mac.

There are a few steps you can try. Rebuild the affected Mailbox, or all Mailboxes, according to Rebuild mailboxes in Mail on Mac - Apple Support. You can rebuild any Mailbox including All Inboxes, Junk, Trash, Outbox, Sent... etc.

If that doesn't work read If you can’t send or receive email on your Mac - Apple Support. Even though it does not describe that specific concern, the last steps (Remove your email account, then add it back) are often helpful.

First remove: Log out of or remove email accounts in Mail on Mac - Apple Support

Then add: Add email accounts in Mail on Mac - Apple Support

Be sure to heed the Important note in the first document.

Troubleshoot email problems in Mail on Mac - Apple Support is Apple's comprehensive guide but it does not address that specific problem.