hecate

As a noun demigod

is a half-god or hero; the offspring of a deity and a mortal.

As a proper noun Hecate is

the powerful goddess, in Greek mythology, of magic, crossroads, fire, light, the moon, and the underworld. Her Roman counterpart is Trivia.

As proper nouns the difference between morpheus and hecate

is that morpheus is the god and personification of dreams; the son of Hypnos and Pasithea, or Nyx and Erebus while Hecate is the powerful goddess, in Greek mythology, of magic, crossroads, fire, light, the moon, and the underworld. Her Roman counterpart is Trivia.