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Docetism can best be thought of as one of the Christological heresies into which Manichaenism falls.
Docetism is very specific Christological heresy. It is a Gnostic idea that Jesus was never born, nor was he ever matter. Gnostics believed that all matter was inherently evil, and therefore it was anathema to them that God could become matter. In order to avoid this distasteful idea, the Gnostics presupposed that Jesus was merely a "phantasm" an apparation of light that looked like a person. In other words, Jesus only appeared to be a man, which is what docetism means.
Manus, a Persian Philosopher had an entire (if heretical) belief system which included several gnostic ideas. Like the Gnostics, he too believed that matter was evil and therefore God could not be born or incarnate in material form. As such, it is most proper to say that the philosophy / religion of Manichaenism includes a docetic Christology.