While both are members of the family Cyprinidae (carp), and both Koi and Goldfish can have similar colors and similar shapes, they are genetically very different.

Koi are the same species as the common asian carp. Color and fin variations are fairly common in carp, and selective breeding has produced many colorful varieties. While there are many variations in color, fins, and size, they are still the same species as their wild relatives.

Goldfish are related to the wild Prussian Carp, but have been bred domestically for over one thousand years , and now have enough genetic changes to be considered a separate species from their wild relatives. There are no naturally wild members of their species.