Confused about the word koji? Is it the mold or is it the molded rice?
When speaking about the actual mold (Aspergillus Oryzae) you would say the word "koji-kin" - this is the yellow mold that influences flavor and aroma in most sakes and is responsible for breaking the starch molecules into glucose. The steamed rice that gets "sprinkled" with this mold (usually from cans with small holes or mesh) is called "koji" or "koji-mai." So when speaking specifically about "koji" you are talking about the inoculated rice itself.
(On a side note Koji-Kin has a nickname in the brewing industry - "moyashi" which is the Japanese name for bean sprouts. Huh? Yes if you look through a microscope the mold looks like bean sprouts or mushrooms. And without question - if you tour a brewery - nine out of ten times you will see a photo of microscopic "koji-kin" looking very much like a large sprout on the wall somewhere.)