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There is a hierarchy of delineation with these terms, and not understanding them or using them incorrectly will lead to confusion. There are species, and when domesticated, there are breeds within a species, and within a breed there are varieties. Breeding one variety of a breed with another variety of the same breed will still give you the same breed, though the resulting offspring might not be of a variety recognized by a breed standard.
A species is a population of organisms that is interbreeding amongst itself and produces offspring that resemble the parents. If two different species are capable of reproducing, their offspring will be intermediate in appearance, rather than resembling one parent over the other.
When a species is domesticated, people can select small levels of variation, or dramatic changes resulting from single mutations, and through non-random mating, affect the appearance of sub-populations. The result is that these sub-populations have a combination of genes that are not found in the rest of the larger population, and if this new sub-population is capable of reproducing its differences consistently into the next generation, then it is called a breed.
Typically, breeds will have a set standard of characteristics to which individuals must conform, and sometimes these standards do not include variations from single genes (such as coat color). Thus if you have pointers that throw a puppy of an unrecognized color, they may not be accepted into the standard but they have all the other genetic requirements for the breed. They are not necessarily "mutts." They could simply be the result of a mutation which was not preferred when the breed standard was written, and were not deemed desirable to breed further. For example, Dalmations come in black and white, and liver (chocolate) and white. These are the accepted colors. If a Dalmation was born with an additional mutation resulting in further dilution of color, it could look lemon and white. The difference is just one gene, and otherwise it is a Dalmation, but it is not in an accepted color.
There are many genes responsible for the differences in appearance in a breed versus the rest of the species, but fewer than the number of genes that differ between two different species. Within a breed, there can be variations in color, pattern, or feather/fur texture that are the result of an even smaller number of genes. These can be called varieties of a breed. Basically, the varieties all share the same basic "breed skeleton" but are "colored in" differently.
Here's an example -- wolves are the ancestral species from which dogs were domesticated. The difference between a wolf and a coyote, on a genetic level, is greater than the difference between a wolf and a dog (yes, wolves and coyotes can still interbreed, which suggests that they are closely related, but not as closely related as dogs and wolves).
Dogs are domesticated wolves, and during the course of our thousands of years of breeding dogs, people have selected for different traits in their animals. When these traits are concentrated and combined into a sub-population that can reproduce among itself and have offspring that maintain the same characteristics, we have breeds. Thus, for example, poodles differ from other breeds of dog in their body shape and proportions, coat texture, etc. And these characteristics that define a poodle are reproducible if you pair a poodle with another poodle.
Poodles are still a type of dog, and differ to a smaller degree on a genetic level from other dogs than they do from coyotes. Thus poodles are not different enough to be called a species, but are a breed. If you breed a poodle with a collie (another breed), you will still have dogs, but these dogs will be intermediate between their parent species. This is because some of the genes found in poodles are dominant to those in collies, and vice versa. In a sense, they are like a hybrid of two different species, but to a much lesser degree, because the genetic difference between poodles and collies is much smaller than the genetic difference between a poodle and a coyote.
Poodles come in many colors, which are determined by an even smaller genetic difference than there is between a poodle and a collie. In many cases, the differences in color are the result of just one gene. I don't remember if white poodles are a dominant or recessive mutation, but let's just say they are dominant. And let's say that black is recessive to white. If you breed a black poodle to a white poodle, the genes that result in "poodle" are found in both parents, so all the offspring will be "poodles." However, the color will be dependent on which single gene is expressed visually -- black or white. Thus breeding together different varieties of a breed that are different because of just one or a few genes will not result in the degree of "mixing" that you'd find if you bred a poodle with a collie.
With peafowl, there really aren't any breeds. There are two ancestral species (unless the greens get divided up further) -- the India Blue and the Green. Breeding the two together results in Spaldings, which are intermediate in appearance to their parents, based on which genes are dominant in one parent species over the other. The IBs have been bred in captivity for a long time, and we do find variations in color and pattern, but these are small genetic differences. Blackshoulder IBs get their color/pattern from simply having two copies of the Blackshoulder gene. Otherwise, there is no genetic difference between what would be called a regular IB and a Blackshoulder IB. They are like different colors of poodles. Such a small degree of difference is not enough to constitute a breed. If someone were to selectively breed peafowl for traits controlled by a larger number of genes -- let's say someone wanted to breed bantam peafowl -- then perhaps they would become a new breed. But otherwise, there is no "standard" for the colors of peafowl because they either have it or they don't.
OK, have to get to class....catch ya later.