Just to clarify terminology, perhaps best explained through my family experience:
My grandfather was Cherokee. His parents were Cherokee, he was born and raised in the Cherokee Nation. There was no document that made him or his parents Cherokee, he was simply known and accepted by his tribe as such. If you asked him if he was Indian he would have said "Yes."
In 1907, he was identified and enrolled by the Dawes Commission (and the Cherokee Nation) as a Cherokee person eligible for an allotment of land in Oklahoma and granted U.S. citizenship. HIs name appears on one of the Final Dawes Rolls so he was an enrolled Cherokee. Delaware and Shawnee people who had been forced to move into the Cherokee Nation after the Civil War were also enrolled as Cherokee. Cherokee people who had married people from other tribes and were living in that tribes territory were enrolled by the Dawes Commission as Creek, Choctaw, and so on.
My father was neither a Cherokee by simple recognition or by enrollment. He was not alive before the Cherokee government was dissolved by the United States in 1907 and was not alive in 1907 to be enrolled by the Dawes Commission. He did not consider himself to be an Indian. Although he was eligible to register as a Cherokee citizen when the tribal govenment was reconsitituted in 1976, he chose not to do so. He remained a Cherokee descendant.
I am registered as a citizen of Cherokee Nation. I also do not consider myself to be an Indian nor do I consider myself Welsh, German, Scots, or English although I have ancestors who were all of those. Because my grandfather was enrolled on the correct Dawes Roll, I was eligible to register with Cherokee Nation and be recognized as a citizen.
All Federally-acknowledged tribes have a "base roll," a list of people from whom a person must be descended in order to be recognized as a citizen. Some current tribes use the words enrolled and registered interchangeably when referring to their citizens. Many tribes have requirements for citizenship in addition to descent from an enrolled person.
Tribal identity could be very fluid in the historical tribes. Most tribes willingly accepted and adopted people from other groups, and once accepted you simply were whatever tribe you were now accepted into. Only when the Federal government, money, and control of land entered into the mix did the need for a formal enrollment process arise.