Within the crystal and mineral community, the name Onyx is often used to describe Calcite, usually Banded Calcite, but true Onyx looks very different to what most people think of.
This confusion has probably arisen due to the difference between the commercial stone or building industry, and the gem and mineral world. Within our gem and crystal community, the term Onyx is reserved solely for use to describe black and white parallel banded Agate, a variety of Chalcedony, which is microcrystalline (crystals that cannot be seen with the naked eye, only through a microscope) Quartz. The image below shows the gemstone Onyx, images from geologylearn.blogspot.com:
However within the building and interior design industry, Onyx is used to describe a much softer calcium carbonate stone - what we know as Calcite. Various names are used to describe this form of Banded Calcite, including Pakistan or Mexican Onyx (depending on it's place of origin), Pakistan Jade (which is a total selling ploy), Onyx Marble, or even Egyptian Alabastar. The soft orange tones of the Mexican variety as seen in the bowl below are caused by iron oxide, the same thing that colours what we call Golden Healer Quartz.
It can also be found in shades of brown, red, pink, green, yellow, black and even blue from Argentina. This variety is usually sold under the name Aquatine Lemurian Calcite, to differentiate it from the more common Blue Calcite from Mexico and Madagascar, but it is sometimes sold as Blue Onyx. Some dishonest wholesalers from China are even marketing this as Aquamarine. However be aware of sellers passing off dyed Agate as Blue Onyx too!
Banded Calcite is relatively soft, and easily carved, which is why we often see fancy lamps, bowls, even cups carved from it.
The name Onyx comes from the Greek word Onux, which translates to "fingernail". This is believed to come from the Greek story of the mischievous God of Love and Attraction, Eros, approaching Aphrodite whilst she slept on a riverbank. He used one of his magical arrows to trim her fingernails, and they fell, but because no part of a god is allowed to die, they were turned to Onyx.