The theories about the Earth being the center of the universe, and the Sun being the center of the universe are very similar. The theory about the Earth being center of the universe, or the geocentric theory, suggests that the Earth is the largest object, located in the center of the universe, and every other object such as the Sun, Moon, planets, stars are orbiting around it. The theory is wrong, and the only thing that it got somewhat right is that the Moon is orbiting around the Earth.
The theory that the Sun is the center of the universe, or the heliocentric theory, suggests that it is the Sun that is the center of the universe, not the Earth. According to this theory, the Sun is the largest object, it is located in the center of the universe, and all the objects such as the Earth and the other planets, stars, moons, are all orbiting around it. The theory is wrong, though it has to be said that it is a big step forward, and while it is not accurate about the universe as a whole, it is very close to how the solar system works.