How do I tell if this sapphire is real?

There is no easy test you can do on it without the risk of damaging the surface of the stone. Normally you can test a sapphire by determining its hardness. Sapphire is a form of corundum which has a hardness of 9 on a scale in which 10 is diamond. So if it is a sapphire it would easily scratch glass and even quartz. (If not, you could damage some of the facets.) The slight change in color is interesting. Some stones do have different colors when viewed in different directions. That would be a distinguishing factor, different than glass. You best bet would be to take it to a GIA (Geological Institute of America) certified jeweler. And just ask what kind of stone it is. What they would do is expose it to UV radiation (black light - short wave). Many artificial stones are "doped" with dyes that cause them to fluoresce brightly. They would also look for inclusions in the stones. Glass and artificial stones grown in laboratories are very clean and without flaws. Natural stones tend to have other mineral grains or inclusions of gas or other fluids. They would be visible when viewed under a microscope.