When speaking about Native Americans, what is the difference between an Indian tribe and an Indian Nation?

There is no distinct difference between an Indian tribe and an Indian nation. Before America was settled by Europeans, each tribe was self-governed and operated as a separate nation — with separate leadership, customs, laws, and lifestyles. From time to time, various tribes waged war against each other. It could be argued that "tribe" is an Anglo-American word, but Native Americans will refer to their people as a "nation." You might hear a reference to the Cherokee Indian tribe but then notice on their official Web site the term, Cherokee Nation. It's the same thing.
Today, the United States continues to recognize the rights of about 560 tribes to self-govern and supports their tribal sovereignty. These tribes (or nations) possess the right to form their own government; to enforce laws; to tax; to establish membership; to license and zone; and to exclude persons from tribal territories. Tribes are held to the same limitations as states (they don't have the power to declare or engage in war, conduct independent foreign relations, or create their own currency).