I've only come across a handful of Cherokee potters and only a very few pieces of their work. Some of the potters seem to be located in Oklahoma (at the western end of the Trail of Tears) and some are in the area of the Smoky Mountains and southern Appalachians. Today's Overmountain Victory National Historic Trail follows part of a trade route through the southern Appalachians and Smoky Mountains that the Cherokee established long before the Europeans arrived. Those mountains had been their homeland for hundreds of years. The British, French and Americans were a pain but nothing they couldn't adapt to. But then came Andrew Jackson, an American president intent on stealing the land out from under them.
Jackson pushed the Indian Removal Act through Congress in 1830. The Indian Removal Act broke every treaty the US Government had ever signed with the Cherokee, Muskogee-Creek, Choctaw, Seminole and Chickasaw tribes. They were rounded up and shipped west, beyond the bounds of most "American" settlements at the time. What happened on that journey is the story of the Trail of Tears.
Beyond the shame of the Trail of Tears is the fact that most of the tribes so displaced were more civilized and better educated than the Europeans who flooded in to take their land and whatever else they left behind. Between 1831 and 1837, the government of Andrew Jackson forced the removal of about 46,000 Native Americans from the southeastern states and opened some 25 million acres of land for settlement by whites.
That doesn't mean the shooting stopped in 1837, or that all the members of the tribes abandoned their property and went west. Some folks from each tribe remained where they were. All they had to do was give up their ancient ways, accept white man's law and do everything like a white man of the time would. Where that concept failed them was so many of the white men of the time were either lone swindlers or members of organized criminal syndicates. Many of those who stayed behind were soon robbed of their land and any other property of value they may have had. Quite a few were simply shot and buried, and title to their land fraudulently signed over at the white man's courthouse.
The Indian Territory the tribes were sent to was land set aside by Congress and guaranteed to the tribes in perpetuity. Then in 1906 Congress reneged on those official agreements, too, and forced open much of Indian Territory for white settlers. A few years later Indian Territory became the Great State of Oklahoma.
From what I have seen, like some Navajo potters, Cherokee potters seem to prefer a finish that is more corrugated or with the coils showing. Certain elements in their decoration are essentially universal across the continent, like hand prints, spirals, basket-weave patterns and corrugation. Some Cherokee potters also like decorations that are similar to Navajo carpet designs. Their clay also fires brown with darker fire clouds. I have yet to see any painted Cherokee pottery.