The federal government has certain obligations to these tribes and tribal members. The United States recognizes that there are Indian tribes with which it doesn't have special obligations, and it also recognizes that there are individual Indian people who aren't members of a tribe. State recognized tribes are eligible for some federal programs. Indians who are not members of a tribe can be eligible for certain federal programs if they can establish that they have an Indian cultural identity, and having Indian ancestry does not automatically mean that you have such a cultural identity. For the purposes of the U.S. Census, individuals can declare their race as whatever they consider themselves to be.
States can recognize Indian tribes according to the state's own definition.
The federal government recognizes these state recognized groups as Indian, it just does not have any special relationship with them or obligations to them. Traditionally, Indian communities defined their members according to an individual's cultural identity rather than genetic background. A person who is born and raised in a community will obviously share the cultural identity of that community. Many Indian societies also had procedures for inducting outsiders into the community. These procedures usually involved, at least in part, the outsider adopting the culture of the community.