Llewellyn posts an intriguing blog asking if all gods are the same. It’s a particular good clarification of the difference between correspondence and equation.
It comes down to this: just because Odin, Mercury, Hermes, and Quetzalcoatl share correspondences, this does not mean that they are the same person. Think of it this way: Your professor, your high school teacher, your doctor, and your psychologist all share certain qualities. They’re intelligent, insightful, helpful, and professional. These are correspondences. But your professor, your high school teacher, your doctor, and your psychologist are all probably different people.
In my own view, Mercury isn’t even Mercury, by which I mean the god Mercurius isn’t the same “person” as the planetary power of Mercury.
But from another perspective, Mercury, Odin, Hermes, and Quetzalcoatl are instantiations of the same ultimate power. The distinction is between the Platonic idea of god and daemon. The god is transcendent, beyond matter, perfect and ideal, and not subject to change or influence. But those gods shine down into the world, and as they do so they manifest as intermediary beings: daemones who communicate between humans and the divine.
So your teacher, professor, doctor, and psychologist are all different people, but they’re representing a particular ideal: teaching and helping you to be a better self. That ideal doesn’t change and isn’t a “person,” but insofar as each of these people represent that ideal, they are “the same.”
It’s complicated and sticky, because it all gets into the concept of “identity,” which is a philosophically complicated notion. One of my favorite YouTube channels addresses this issue very clearly and well: