Rubies specifically are red sapphires. Both are a mineral called corundum. Emeralds and diamonds and most other gems have their own specific chemical compositions and structures. Diamonds for example are just carbon (but structured differently from graphite and coal doesn’t have much structure) emeralds are a type of crystal called a beryl. It’s a silicate made of beryllium and aluminum (Be3 Al2 (Si O3)6)
Of these gems mentioned, they are naturally clear and get their color from an impurity from another element if they have it with the exception of emeralds, which are green even when pure.
Quartz for example has all sorts of names. Rose Quartz, Herkimer Diamond, Amethyst, they are all just silicon and oxygen with an impurity giving it color. Look at the chemical compositions for the minerals that make them up to assess if they are the same thing.
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