German Shepherd Dog was originally bred in Germany in a town call Alsatia. During the WWII the allies were impressed with the breed and wanted to bring it to England and breed. But Europe did not accept the term "German" against the breed name. They remained it Alsatian. There is NO difference between the two except the names. They have the same Characteristics. In today's world the name German Shepherd is fully accepted even in the European countries.
I don't think there is any difference
Alsatian is the correct name of the German shepherd breed. Not the Belgian, nor any other. The original big headed, good natured, family oriented German shepherd. Lovely animals, don't you think?