Syncretism is the belief in the merging of various schools of thought. It is especially associated with the attempt to merge, analogize or assert the underlying unity of several originally discrete traditions, especially in religion and mythology.
Syncretism is common in literature, music, representational art and other expressions of culture.
Some religious movements have embraced syncretism while others have rejected the practice as devaluing real distinctions. Syncretism was a major feature of Greek and Roman paganism; imagining themselves as common heirs to a very similar civilization, they identified characters from Greek mythology with similar characters from Roman mythology. See Roman/Greek/Etruscan equivalency in mythology The fits were sometimes good, sometimes not as good; Diana is a better match for Artemis than, say, Ares is for Mars.
From these identifications, the classical world acquired the habit of identifying gods of even more disparate mythologies with their own. The Egyptian god Amun deveolped into Zeus Ammon after Alexander the Great conquered Egypt. The Greek gods Apollo and Dionysus were imported into Rome; given this precedent, the Romans saw no hindrance to the worship of Isis and Osiris (Egyptian) or Mithras (from Hinduism or Zoroastrianism). Likewise, when the Romans encountered Celts and Teutons, they mingled these Northern gods with their own, creating Apollo Sucellos (Apollo the Good Smiter) and Mars Thingsus (Mars of the war-assembly), among many others.