Please explain why they are or are not the same.
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The vast majority of gemstones are minerals and are thus crystalline (meaning they have an orderly internal structure). There are a few exceptions if you use a general definition of gemstone. Some of the exceptions are amber, which is not a mineral at all, pearls are also not minerals, jet, a form of coal is not a mineral, and obsidian which is a volcanic rock and not a mineral.