There are a lot of overlap between theses words.
Rocks are made of minerals, which can be crystals, which if big enough could also be gems (gems and gemstones are synonyms), or could also form Geodes.
Rocks are just any solid material you encounter and are made up of a variety of minerals depending on where and how they formed.
Minerals are also a very broad class, minerals are “a solid inorganic substance of natural occurrence”. So all rocks are made up of minerals, and minerals describes essentially everything that isnt made by living things or refined by human activity.
Crystals are mineral depositions. When some minerals solidify or get deposited by water, they form in an orderly, crystalline structure based on how each molecule lines up or stacks up. This can lead to specific shapes, or specific colors, or strength properties based on the specific properties of each mineral.
So the salt crystals that form when salt water dries are crystals, the quartz crystals that form when silica (silicon oxide) is deposited neatly.
Gems are just crystals of value, crystals that are valued because of their size, or their color, or their transparency.
Geodes are like special crystals/rocks combined together.
In some rocks, there will be an opening or pocket inside the rock from one mineral or another getting dissolved away or simply because of how the rock formed like pockets in lava rock
In that opening, groundwater will gradually seep in, and over hundreds or thousands or even longer that groundwater will bring in other dissolved minerals, which can then deposit on the walls of that cavity, and slowly build up crystals on the walls of the opening creating a geode.
By that definition, the “Crystal Caves” in Mexico one could argue that those caves with massive, multi-ton crystals are technically giant geodes. But that’s not typically how the word is used.
But yea, all those words have A LOT of overlap, they’re just words for specific kinds of formations.
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