Chorasmia

A peculiar feature of the Amu Darya is the fact that all of its water did not always flow into the Aral Sea. At certain periods one branch swerved, shortly after having reached the apex of the delta, northwest and then southwest, passing by medieval Urgench. Called Uzboy, this branch then pursued the southwesterly course all the way to the Caspian Sea, which it entered through a wide coastal plain south of Krasnovodsk (Turkmenbashy)...In 1576 the river swerved back toward the Aral Sea, and the definitive decline of Old Urgench, thus deprived of its water supply, is by some historians attributed more to this natural cause than to devastations wrought by the armies of Genghis Khan and Timur.

From 1221 to 1576ish the Amu Darya flowed into both seas. There was a change in the river in 1221 because the Mongols destroyed a dam on the river. At different times before then, the water flowed into both seas, or just the Aral Sea. Finally, the Seleucides considered building a canal between the Caspian and Black Seas so that merchandise could be transported up the Amu Darya (which was obviously flowing into the Caspian at the time), across the Caspian and through the canal to the Black Sea. It's amazing to think of shipping going on across those areas!

http://amiralace.blogspot.com/2005/09/aral-sea-in-history.html