Red rice is rice that is colored red due to natural anthocyanin content. It is usually eaten unpolished or partially polished, and has a red bran layer, rather than the more common pale brown. Red rice has a nutty flavor. It has the highest nutritional value among rices eaten with the bran intact.
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Red rice in the context of Brown rice
Brown rice is a whole grain rice with only the inedible outer hull removed. This kind of rice sheds its outer hull or husk but the bran and germ layer remain on, constituting the brown or tan colour of rice. White rice is the same grain without the hull, the bran layer, and the cereal germ. Red rice, gold rice, and black rice (also called purple rice) are all whole rice with differently pigmented outer layers.
View the full Wikipedia page for Brown rice