Most of the Japanese-style rice sold in the USA is grown in California. California has been producing Japanese-style rice since the times of the Gold Rush!
Most of the rice grown in California is the medium-grain Japonica cultivar, as opposed to the long-grain Indica cultivar. Calrose is a type of Japonica rice that was developed by the University of California-Davis in the 1950s.
Botan, Kokuho Rose, Nishiki, Shirakiku, etc. are brands of rice.
Koshikari rice is a "superpremium" Japonica rice that costs more than standard premium brands -- some brands are grown in California; some are imported from Japan. Tamanishiki and Tamaki Gold are several brands of koshikari rice.
"Musenmai" means the rice doesn't need to be washed before cooking. (In the old days, rice was coated with talc during processing, and needed to be washed before cooking. In the 1950s-1960s, when people realized that talc could contain asbestos, rice mills substituted cornstarch, but the rice still needed washing to remove the excess starch. New musenmai rice is processed using tapioca, which apparently doesn't stick to the milled rice.)
You can read up more about the different varieties of rice at: RICE 101
BTW, my favorite rice is the premium Kokuho Rose True Koda Varietal (pink label), which I wash before cooking. (There is also lower-grade blue-label Kokuho Rose Calrose rice.) I tried several brands of superpremium rice and was not impressed by the difference in flavor or texture.