Suddenly my iPhone and iPad are not syncing messages. This just

If it is only SMS (regular text) messages that aren't syncing, go to your iPhone's Settings/ Messages and verify that Text Message Forwarding is enabled for your iPad (even if it is, try turning it off and reset both devices, then turn the setting back ON).

If some messages sync, but not all, try signing out of iCloud on both devices and reset both devices, then sign back into iCloud (iPhone first, then iPad) and verify that your iCloud settings are correct on both devices.

If no messages are syncing, even iMessages, are both devices signed into the same iCloud account?

By your signature you indicate that your iPhone is on iOS 11.4.1, what revision of iOS is your iPad at? Messages in iCloud was released in 11.4, but you have to enable it on all your devices if you expect them to remain in sync. Maybe that's the issue, have you done this?

Keep all your messages in iCloud - Apple Support

Go through the steps in

https://support.apple.com/en-us/HT204681

Under those conditions, did your iPad "catch up" on any messages that came to your iPhone while your iPad had no internet connection? Or are you saying the problem started only after you got home?

Another thought ... go to your iPad's Settings/Messages/Send & Receive and check that it is set up the same as your iPhone (i.e. the iPad can receive messages via your phone number and/or email ... make sure this is the same as your iPhone).