Slight modification. It appears that Galileo believed the sun to be one of many stars. I believe Copernicus taught true heliocentrism, that all heavenly bodies, including of course the stars, orbited the Sun.
It had slipped my mind that the original heliocentric model also posited a stationary sun at the center of the universe. Thanks for reminding me! I could be wrong, but I'm fairly certain that, although he did hold that the sun was one of many stars, Galileo was at most vague about the centrality of the sun. Whatever the case, it was not until the period between Kepler and Newton that it was widely accepted that the sun as well was neither fixed nor central.