Jasmine rice is a long-grain, fragrant type of rice common in Asian dishes, especially those from Thailand. It is available in both brown and white form. These aren't different varieties but rather the same rice in different stages of milling.
Rice is actually a grass that sprouts clusters of spikelets instead of flowers. Each spikelet contains a husk hiding a grain of rice, which is really the endosperm of the rice seed. The germ, a small chunk at one of the tips of the grain, is the embryo.
All white rice was originally brown, and all rice is milled to some extent to remove the outer husk or hull. Rice that doesn't undergo anymore milling is brown rice, while those grains that have the bran and germ removed become white rice. A Japanese variety of rice that is partially milled so that the bran is gone but the germ remains is called haiga-mai.
Removing the bran and germ from rice also removes the vitamins. Colorado State University says beriberi, a form of thiamin or vitamin B1 deficiency, is more common in areas that rely on refined white rice that hasn't been enriched with vitamins after milling. Most white rice in the United States is enriched.