Anishinaabe is what these peoples call themselves, and the grouping is theirs rather than an outsider's. At its core is the Council of Three Fires, the alliance of the Ojibwe, the Odawa and the Potawatomi, whose relationship is described in their own accounts as three brothers with distinct responsibilities: the Ojibwe as keepers of the faith, the Odawa as traders, the Potawatomi as keepers of the fire.
The wider term takes in the Mississaugas, the Saulteaux, the Nipissing and the Algonquin. Their territory runs around the upper Great Lakes on both sides of the Canada and United States border, a border drawn across them rather than by them, and the migration story recorded in their oral history brings them west from the Atlantic coast to the place where food grows on water, which is wild rice.
Ojibwe and Chippewa are the same word spelled two ways, the second being the form that entered United States treaty language, which is why both appear in legal documents and why the same nation can be listed under two names in two countries. Wild rice is not incidental to that story. Manoomin is food, it is the destination named in the migration account, and it is at the centre of present legal argument in Minnesota and Wisconsin over water quality and treaty rights, so a sacred plant is also a matter before the courts.