The grading systems you will see are inventions of breeders, dealers, hobbyists, and other folks. As far as I can tell (koi breeder for over 15 years) there is no standard.
Koi are bred all over the world. They are sorted and sold many times before reaching the hobby pond. The process begins with the breeder. The breeder sorts (culls) the koi into several grades, the goal being to get the best price for the best fish. Once sold to a distributor, they might be sorted again. Sold to a dealer, they once again might be split into more grades. You can call them anything you like. So can the fish dealer. However, most hobbyists looking to spend several hundred or thousand dollars on a fish will know a good deal about the fish. What I am trying to say, I could price my fish any way I want, but if I want to sell any of them, I must be able to justify the price to the potential purchaser.
The sorting (culling) process, called "sembetsu" in Japanese begins sometimes at the ripe old age of three days for some breeds. "Sembetsu" is better translated into "sorting" than "culling". I am now in my ninth year of study with respect to grading koi on my breeding farm. I have spent many years studying under Japanese masters to try and learn the subtleties of the process.
Fingerlings are graded almost constantly. At my farm, we grade fish once a week. Not all the same fish, but as each batch is brought in, they are sorted. In every case but for the youngest fish, these might have been sorted as much as ten times before, depending on age.
The offspring seldom look like the parents. Very careful breeding will help improve the chances of obtaining a good one or two from the hundreds of thousands hatched. Goes something like this:
250,000 eggs, 100,000 fry stocked, 60,000 fingerlings harvested. From the 60,000, about 2000 to 3000 might be "keepers" in the first sort (separating keepers from non-keepers). Grow maybe 3 to 6 months, harvest the 2000 keepers and sort again. Maybe 500 throw aways, 1000 sold as cheapos, 500 put back to be graded next time. 500 brought in another 3 to 6 months. 400 sold, some as cheapies, some as "select" or "A" grade. 100 put back to grow some more. By now these are getting kinda big, maybe 6 to 8 inches or more. 100 brought in, 96 sold as fairly good fish, maybe "AA", and 4 put back for another year. 3 then sold as very nice koi, 1 kept to be watched for either a good "tategoi" ("keep koi") or perhaps as a brood animal. Maybe sold off at the age of 3 or 4 years for substantial money ($1000+). So, out of 1 million koi, maybe 4 very good ones produced. Yield varies with breed, quality of the brood stock, and a few other factors (how many turtles in the pond, birds, etc.).
All of my koi are "domestic". Horrors, they must all only be worth $0.25 each then. No, I just bred them all here (Brazoria County, Texas). Most of the brood fish were "Japanese" (Hatched in Japan, product of Japanese hatcheries). The offspring sell cheap or expensive, depending on the quality of the fish. They get entered in shows, win prizes, etc. Koi judges use their eyes to judge the koi, they got no idea where the koi came from (not supposed to, anyhow).
With showa and utsuri we sometimes start at three days of age and the fish are less than 1/4" in length. With most of the fish, we wait till they are about 60 to 90 days old and approaching 2". Part of the reason for the long wait is that the older the fish, the easier they are to sort. Much of my "sorting crew" is very inexperienced and they need a bigger fish to work with. Part of the reason is I have a market for the "culls" if they are big enough. Not as ornamental fish, but as feeders and bait fish. The object of the initial sorting is to separate "keepers" from "non-keepers". This cuts down on the feed bill and allows for more rapid growth of the keepers. By winter we will be sorting fish into "low and high" grades and placing them into different ponds.