Natural turkeys have been minimally processed, with no artificial ingredients or coloring added.
Certified organic turkeys have been fed organically grown feed all their lives and never treated with antibiotics. Many small growers and free-range growers follow organic practices, but may or may not be certified organic.
Free-range generally means the animal is allowed to be outside at least part of the time. For some growers this may be a short time, other growers allow the animals to roam a large area, with access to shelter as the animal desires. Look into the practices of the specific grower if this is important to you.
According to the American Livestock Breed Conservancy, heritage turkeys must mate naturally, have a long outdoor lifespan, and a slow growth rate. They tend to be smaller than commercially bred turkeys, with more evenly distributed meat and a stronger turkey flavor.
Kosher turkeys are prepared under rabbinical supervision. Many people like the flavorful poultry that often results from the salting that is part of koshering meat.