The word "crystal" is very confusing in English language. It is used for two very different materials, both of them are sought after in jewellery. It would be a lot less confusing if there were two different words for those two materials, like they are in some languages...
What do we call crystals? First of all, there are crystal stones. Not all stones are crystals. When we say that a stone is a crystal, we mean that it has a crystal structure. A crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a unit cell, a set of atoms arranged in a particular way; which is periodically repeated in three dimensions on a lattice.
This crystal structure is actually visible in a rough crystal stone, such as diamond, quartz, amethyst or aquamarine (and others). Natural crystals look as if they were cut and polished. However, this is their natural form.
Natural crystal or
rock crystal is quartz. This one is probably most confusing term that not everybody knows about...
The word crystal is also used for glass. However, not any glass can be called crystal. Most popular crystals are made by Swarovski company if speak of jewellery. Swarovski crystals do not have a crystal structure. Crystal glass is made by a special formula. Many companies make crystal glass. However, the formulas very. Swarovski company is very protective of their special formula.
Swarovski crystals (or any crystals made for jewellery) often look as if they have a crystal structure. This is just a cut though. They are faceted to maximize the sparkle. The shape has nothing to do with internal structure of the material.
What crystals do you prefer: natural or Swarovski?