Hello, SueAppleSupport.
You've done some great narrowing down of the issue on both devices, so thanks for doing that ahead of time. From here, our advice would be to remove the mail account from the Mail app on both devices, restart them, then add it back. Sometimes, that can help straighten out syncing issues.
Remove email accounts in Mail on Mac - Apple Support
- "In the Mail app
on your Mac, choose Mail > Preferences, then click Accounts. - Select an account, then click the Remove button
"
Add and remove email accounts on iPhone - Apple Support
Remove email accounts
- "Go to Settings
> Mail > Accounts. - Tap the email account you want to remove, then do one of the following:
- If you’re removing an iCloud email account: Tap iCloud, tap iCloud Mail, then turn off “Use on this iPhone.”
- If you’re removing another email account: Turn off Mail.
- Note: To remove the email account from all apps on your iPhone, tap Delete Account."
Add email accounts
"The first time you open the Mail app on your iPhone, you may be asked to set up an email account—just follow the onscreen instructions.
To add additional email accounts, do the following:
- Go to Settings > Mail > Accounts > Add Account.
- Do one of the following:
- Tap an email service—for example, iCloud or Microsoft Exchange—then enter your email account information.
- Tap Other, tap Add Mail Account, then enter your email account information."
Remember to restart both devices in between removing and adding back (Restart your iPhone & Shut down or restart your Mac - Apple Support). Let us know if we can help with anything else at all or if this doesn't settle your issue. Thanks and have a fabulous day!
