They are the same.Alsatian means 'from Alsace' Alsace lies on the border of France and Germany and changed hands between the two several times in history.At the time of World War I it was German but the French regarded it as French.That's when and why this German breed was renamed.We started calling it Alsatian because France was on our side and anything German was hated.The dachsund and the Pomeranian were not so fortunate, and fell out of favour.There are stories of dachsunds being put down because they were 'German'.
(The Royal Family changed its German family name to Windsor ,for the same reason, at this time.)
The shape: it's the show breeders of modern times who insisted upon breeding for the 'squatting bitch' look, with the hindquarters set low. As late as 1960, the straight back was still generally accepted. That's how the breed was originally.Back in 1901, when the first breed club was established in Germany,it was straight-backed as well as being a 'squarer',shorter bodied, dog. It did change a bit thereafter but was always straight backed.(Purists have 'reconstructed' the original square, straight backed, shape and called the result the Shiloh Shepherd).