The term breed has many different meanings based on the species it is being applied to. All turkeys except Ocellated turkeys are the genus species Meleagris gallopavo. They only differ in the sub species.Um, no, the species is turkey (Meleagris gallopavo). There are different breeds created from a species (by humans) and different varieties of a breed. In this case I think the OP is trying to figure out the subspecies.
The APA classifies all turkeys as the breed turkey and sorts them by varieties. They currently only recognize 8 of the many possible different varieties.
How the term breed is used for turkeys has nothing to do with how it is used for dogs or chickens or cattle for that matter.
If the varieties of turkey were actual breeds, one would expect that crossing two of those different "breeds" would result in a hybrid. Several examples of this not being the case is that if you breed a Sweetgrass tom to a Royal Palm hen, all of the offspring are Sweetgrass. It does not produce a hybrid.
Another is that if you breed a Bronze tom to a Narragansett hen, all of the offspring will be Bronze.
Turkeys are all much more closely related to each other than chickens are.