Basically, the new Messages in iCloud feature is the same for Messages as Apple did with Photos when introducing iCloud Photo Library.
Before iCloud Photo Library, any photos you took were stored on your device and only put into iCloud as part of the backup of your iPhone or iPad. Thus when restoring to a new iPhone or iPad you could see your photos again. The problem with this is that if you wanted a photo from your iPhone on your iPad, you would have to transfer it over somehow and then it would be included int he backup of that second device as well thereby using even more of your iCloud storage space.
Enabling iCloud Photo Library takes all your photos out of your backups and stores them in iCloud separately to your iPhone and iPad device backups. Each device then just looks at the photos in iCloud and can see them all. Your individual devices then pull down high res copies of each of them only when required. This allows your phone to optimise its onboard storage.
The same thing is now happening with Messages. All your Messages will be stored separately in iCloud and not in any of your device backups. This allows no duplicates and saves you and Apple themselves storage space.
It seems to make sense to me.
In short, the difference is where in iCloud the media is stored:- As part of each device backup or separately enabling smoother and more efficient sync between devices.