The Earth centered theory about the universe (geocentric theory) is the oldest one recorded. This theory suggested that the Earth is the largest object in the universe. It is the center of the universe, and all of the other objects, like the Sun, Moon, planets, stars, are orbiting around it.
The Sun centered theory about the universe (heliocentric theory) has been developed in the late Middle Ages. This theory suggested that the Sun is actually the center of the universe, not the Earth. That the Sun is the largest object in the universe, and the Earth, Moon, planets, stars, were all orbiting around the Sun.
In reality both of these theories are wrong, with the heliocentric theory being closer to the reality, or rather to how our solar system works, not the universe. Neither the Earth nor the Sun are centers of the universe. They are both just small parts of a much larger picture, where the Sun is the center of the solar system, with the objects in the solar system orbiting around it, while the moons orbit both around the Sun and around their planets. The Sun though is part of a galaxy that has its own center, so the Sun together with all the other objects that orbit around it, orbit around the center of the galaxy.
