So far each of the identified dominant white families have been a separate mutation, and in most cases the originator is recent enough that they are known individuals. The version of dominant white that originates with Puchilingui, W5, is known for producing a pretty wide range of sabino-like patterning as well as truly white horses.
With horses like these, it is easy to understand why breeders use the term sabino when advertising their horses, rather than their technical classification. Mare owners looking to produce pinto patterned foals know what a sabino looks like, and dominant whites of this type produce what looks like a sabino. The “proper” genetic term can be, at least in that kind of setting, unintentionally confusing.
In informal settings, it is likely that dominant white horses will continue to be referred to as sabinos. That is what they look like, and that is the term many horse people understand. They are very different though, so in formal settings where genetics are being discussed they deserve their separate names. That topic probably deserves its own post, though.
Another quick note about Sato, though. The close-up at the top of the post shows the blue segment in his eye really well. Although dark eyes are more common, a number of the dominant whites have had blue eyes. This happened with some of the sabino white Walking Horses, too, though it appeared to be less frequent. (The topic of blue eyes in Walkers is pretty complex, so that will have to wait for the volume that covers light breeds.)