Prince of Persia: Warrior Within/WMG

Sands of Time Prince's Generic Rage persona was the Dahaka's fault
Not just because being forced to run for years, no one believing him, jaded him up. The Dahaka was also able to directly corrupt him somehow, and do it very thoroughly. Maybe it's not the only one of its kind, and reproduces through converting the people it chases. Being exposed to the Sands made the Dahaka in him sort of separate from what was left of the rest of him, resulting in the Dark Prince, a combination of Dahaka and sand monster.
 * All but confirmed in The Two Thrones, where Kaillena all but says something to that effect in the opening levels.

The Dahaka is a sand monster
It can't pass through water, dies when it falls into the sea, and is clearly hurt by the Water Sword. Now, does a beast which represent fate itself sound like it would have those vulnerabilities? More likely, it's a sand monster impersonating the real Dahaka, of which there are only legends.
 * Actually, water and sand appear to be symbolically opposed elements in the PoP-verse. Sand represents time and entropy; water represents life and renewal.