The Sioux Nation(s) are a group of Indian Nations collected under one rubric due to language, associations, traditions and an Act of Congress that defined them as one "Nation". The three tribes are the Lakota, the Dakota, and the Nakota.
The Dakota (Santee Sioux or Easter Sioux) had their traditional homelands in and around the Great Lakes regions of the North East, most concentrated in and around Minnesota ('Smoky Water' in the Dakota Dialect). Unlike the Lakota, the Dakota were traditionally a woodlands people, who both hunted and used limited agriculture. Upon contact with Europeans, the Dakota became heavily involved in the local fur trade. During the 18th and 19th centuries, competition with other tribes and trade restrictions enforced by the Hudson's Bay Company relocated the Dakota to Southwestern Minnesota and threatened their traditional lifestyle. By 1862, the Dakota were confined to a small area of Southwestern Minnesota upon which white immigrants were beginning to encroach. Although some began to embrace this much more sedentary, agricultural based lifestyle, most became dependent on U.S. Government food supplies. As the fur trade in Minnesota dried up, the Dakota became heavily indebted to local fur traders, who began confiscating government subsidies as payment. In 1862, in response to this situation, large numbers of Dakota rose up in insurrection. After the failure of the insurrection, the Dakota were either put on reservations in Minnesota, dispersed westward into the Dakota Territory, or permanently resided north of the border in what would become Manitoba.
The Nakota or Yankton Sioux were a small subset of the Sioux Nations.
The Lakota (also Teton) Sioux are the largest of the three subsets of the Sioux Nations. They are the stereotypical "plains indian" "Movie Indian", complete with a complex horse driven culture, tipis, and head gear straight out of a John Wayne show.
The Siouian language group is a large family of languages that include the Sioux, the Mandian and the Haditsian. It is a verb last language that uses infixes on the verb to identify the subject (that is, a verb like "to hit" apa is aMapa "I hit"; aWapa, "you hit" and just apa "he or she hits".) Also, Lakota and Dakota have different grammars for women as for men.