The terms used to describe Koi are “class” and “Variety” Breed isn’t used because even if you have two fish of the same variety or class their offspring can be anything. You’ll never know what your getting when breeding fish. It can be fun and exciting.
Here is a photo of one of my Kohaku Koi they ( the orange and white) seem to be everyone’s favorite.
I bought him when he was just about 4 inches long and now look at him. He’s a big eater and loves to look thru the lilies for any morsels hidden amongst the leaves.