When an appraiser examines a cut stone one of the first things they do try to determine the gems physical properties, the way it deals with light as light enters the stone, pleochrysim, double refraction, dispersion, refractive index of the stone and sometimes the specific gravity of the stone. There are about 30 bits of information that can be obtained to positively identify a stone. A good appraiser will look for at least 5 of these bits to make a reasonable guess. The color of the stone is the last thing that they will look for.
Is there a difference in value between natural and synthetic. You bet there is and sometimes the difference if quite dramatic. For example a natural flawless emerald (if there was such a thing) could be worth up to $200,000 per carat where a synthetic emerald could be worth up to $2000 per carat.
If a graduate gemologist simply looks at a stone and tells you what it is, they are only guessing. To positively identify a stone they have to go through the same steps, using the same testing equipment as an appraiser to positively identify a stone. No one can positively identify a gem by its color, because so many other stones can be the same color.