A color of a star is defined as the ratio of its flux through filters that cover different ranges of wavelength, e.g. a blue filter and a yellow filter. The color of a star does not depend on its distance, because the fluxes through each filter are equally affected by distance. However, a star that is moving perpendicular to our line of sight will also change its position in a way that builds up from one year to the next. This is called proper motion. With high-precision measurements of relative positions, we can determine the parallax of nearby stars.
Observed stars have an enormous range of apparent brightness.
Some of this range arises because stars are at different distances. However, stars also have a wide range of intrinsic luminosities. Understanding what determines a star's luminosity, and why the range of luminosities is so large, will be a major theme of the next three weeks.