Hey BillT,
We'd recommend checking to ensure you're signed into messages on both devices with the same Apple ID. If that doesn't help, we'd recommend disabling iMessage on both devices and then turning it back on to refresh and check to see if that helps. You can find steps for that here: Access your messages on all your Apple devices - Apple Support
"Turn off Messages in iCloud
You can turn off Messages in iCloud on all your devices or on your Mac only.
- In the Messages app on your Mac, choose Messages > Settings, then click iMessage.
- Click Settings, then deselect Enable Messages in iCloud.
- Choose one of the following:
- Disable All: Turns off Messages in iCloud on all your devices. Messages are no longer stored in iCloud and are instead stored on each device.
- Disable This Device: Turns off Messages in iCloud on your Mac only. Messages on your Mac are no longer stored in iCloud; on any other device where Messages in iCloud is turned on, messages continue to be stored in iCloud."
Thanks!