If you have an iOS device and a macOS device, you may have noticed that some content in Messages is not synced between these operating systems. The reason is that SMS messages are not synced. So if you get a message on your iPhone/iPad and not on your Mac it’s because it was sent as an SMS message.
Another thing that you may have noticed about macOS Mojave is that in the iCloud preferences you no longer see Messages as an app that you can select to sync with iCloud. Messages is synced in iCloud in Mojave by default. In iOS 12 and below, you will still see Messages as an app that you can select to sync in iCloud, and it should be selected.
Tidbits:
If you are texting with someone from your iOS device who doesn’t have an iOS device (i.e., Android), the text message will be displayed in green instead of blue, and that message is actually an SMS message and will not be synced with macOS.
Using Messages in macOS, you cannot send a text message to a phone number that is not a registered iOS device but you can send a text message to any email address.
John R Carter Sr