The words above are kind of a compound word they carry different meaning depending on the use. For instance you cannot say “I am selling fancy gemstones “,
You have to clarify by saying; “I am selling fancy color gemstones” or “I am selling fancy cut gemstones”.
In diamonds the word fancy is used more than cut or shape style.
Fancy colored diamonds are Diamonds that exhibit yellow or brown color beyond the Z range, or that exhibit any other color.
Fancy cuts or fancy shapes are any cutting style apart from “round out”.
Arch, Cushion, Heart, Marquise, Oval
Pear, Rectangle, Square