sun noun \ ˈsən \ 1 a: often capitalized : the luminous celestial body around which the earth and other planets revolve [...] b: a celestial body like the sun : STAR
Wikipedia states: The Sun is the star at the center of the Solar System.
According to some articles on the web, other stars can be suns as well, if they contain a planetary system.
In common language however "the sun" is typically our star. "a sun" might be other stars as well.
I think most people dont understand and think about the difference and thus think a star is a sun.