Metemphsychosis, like Plato’s theory of transmigration of the soul, is concerned with human reincarnation. Plato “proves” this by showing how knowledge is just “reminding” rather learning anew.
Reincarnation, as in Hindu metaphysics, involves all life forms. A human could be a bird in the next life, which negates the Greek theory of soul.
Metempsychosis is a philosophical term in the Greek language referring to the belief of transmigration of the soul, especially its reincarnation after death. It is a doctrine popular among a number of Dharmic Religions of the East such as Hinduism and Jainism wherein an individual incarnates from one body to another, either human, animal, or plant. Generally the term is only used within the context of Greek Philosophy, but has also been used by modern philosophers such as Schopenhauer; otherwise the phrase transmigration is more appropriate. The word also plays a prominent role in James Joyce’s Ulysses. Another term sometimes used synonymously is Palingenesia.
Reincarnation, literally “to be made flesh again”, is a doctrine or mystical belief that some essential part of a living being (in some variations only human beings) survives death to be reborn in a new body. This part is often referred to as the Spirit or Soul, the ‘Higher or True Self’, ‘Divine Spark’, ‘I’ or the ‘Ego’ (not to be confused with the ego as defined by psychology). According to such beliefs, a new personality is developed during each life in the physical world, but some part of the being remains constantly present throughout these successive lives as well.
Belief in reincarnation is an ancient phenomenon. This doctrine is a central tenet within the majority of Indian religious traditions, such as Hinduism (including Yoga, Vaishnavism, and Shaivism), Jainism, and Sikhism. The idea was also entertained by some Ancient Greek philosophers.
Many modern Pagans also believe in reincarnation as do some New Age movements, along with followers of Spiritism, practitioners of certain African traditions, and students of esoteric philosophies.
The Buddhist concept of Rebirth although often referred to as reincarnation differs significantly from the Hindu-based traditions and New Age movements in that the “self” (or soul) does not reincarnate.