Chalcedony is the mixture of quartz and moganite. Here is where things get confusing: moganite is a subset of quartz. It has the same chemical structure, yet it has a different crystal structure. So basically, chalcedony is a quartz with a mixture of crystal structures. This mixture gives it that lovely waxy and translucent property.
Orange/red chalcedony is often called carnelian, though there is a darker variety called sard (dark red/brown). However, until the Middle Ages, they were both classified under the term "sardion." When sard is mixed with bands of white chalcedony, it is called "sardonyx".
With the exception of "crystal," sardion is the OLDEST known name of a type of stone. Why? Because before the Middle Ages, sardion and sardonyx were more precious than gold and silver, as they were considered the most rare, beautiful stones.
SUPER fun fact: Before the "F" word was invented, medieval Europeans called the act of copulation "Sard."