It's about the two dots at the base of the tails, visible when the wings are spread. Sometimes they are orange but I have also seen them more yellow/brown. Do the differentiate for gender, maturity, or something else?
Karen says: There doesn't seem to be a definitive reason why the two dots might vary in color.
Also, in my research it appears that it is difficult to visually tell the difference between the male and female giant swallowtail....unless, of course, you see the female laying eggs :)