The eggshell is either blue or white. It may have a brown coating applied to the outside of the shell.
Blue eggshell + coating = green
Blue eggshell + no coating = blue
White eggshell + coating = brown
White eggshell + no coating = white
This is looking at it very simplistically; the pigment that makes up the coating can vary depending upon the specific genes involved (and there are multiple).
Likewise, the pigment that goes into a blue eggshell can vary somewhat, causing some chickens' eggs to be darker/lighter or changing the hue a bit. There are genes that whiten up a white eggshell as well, and some that make the shells shiny and others that give them a matte surface.