Derived from the Latin adjective Stygius, from the Greek Stygios, all are related to the River Styx, that river in Greek mythology which separated the land of the living from Hades, the land of the dead.
The name of the river is closely related to the Greek adjective stygnos, “hateful, gloomy,” and this, too, is the meaning most often associated with our adjectival use of the river’s name.