Are red wolves, domestic dogs, wolves and coyotes the same species?

Gray wolf is the ancestor of domestic dogs and coyotes. Coyotes evolved from the gray wolf in the southwestern USA but it is considered a different species. The domestic dog was domesticated from a captive population of the gray wolf but there is no agreement as to whether it is a distinct species or part of the species that is the gray wolf. Some people classify dogs as a subspecies of the gray wolf but that is not universally supported because a subspecies is defined as a regional variant within a species. Domestic dogs do not live in the wild, and it is not restricted to one region, and there is also no way to define a domestic dog morphologically, since the different breeds are so different.

The red wolf is considered a possible hybrid population between the coyote and the gray wolf by some people and it is considered a distinct species by other people. Therefore there is no consensus on the status of the red wolf either.

The definition of a species most widely accepted is that it is one or more populations that either actually interbreed or potentially interbreed and they are reproductively isolated from other such groups. It is well known that coyotes can produce fertile hybrids with the gray wolf. However, they seldom interbreed in the wild so they are not considered the same species since they are reproductively isolated from the gray wolf.  The reason is that they are very different ecologically. Coyotes are smaller lone hunters of small animals, but wolves are larger pack hunters of big game. Their hybrids, known as coy-wolves, are intermediate in size so they are not as good at hunting small animals, since they are less agile than coytoes.  Since they also tend to be lone hunters, they are not good at bringing down large prey either. As a result these hybrids are less capable of surviving than either wolves or coyotes. The hybrids therefore tend to die out over the long run, which means those wolves and coyotes that do not make sure they mate with their own species only will eventually leave no descendants. That is why in the wild, interbreeding between different, even though closely related species are rare, since the hybrids are usually less fit. It is why most individuals, especially females, tend to be very careful when choosing mates, because mistakes can be costly in terms of evolution.  For this reason, even if two species are capable of producing hybrids once in a while, they are considered different species if they do not interbreed freely in the wild and they therefore maintain their ecological differences. Different populations that interbreed freely will tend to become a single species. Since the coyote and the gray wolf maintain their differences by avoiding interbreeding, they are not the same species.

That shows one of the shortcomings of using the genetic species concept. There are better examples, though. Certain minnows are completely interfertile, not only across species lines but across generic ones as well. What geneticists proposed and had the hubris to call THE biological species concept doesn't work for the vast majority of organisms, the ones that reproduce only asexually and the ones known only as fossils. Genetic information can be valuable to the taxonomist but it is only one of the tools that is used.

The species concept used by most taxonomists (although it is not cited as the definition) is the one proposed by C. Tate Regan: A species is whatever a competent taxonomist working with the group says it is. Although it sounds flip, it works.

Producing fertile offspring is the biological species concept but that isn't used much these days; rather species are groups that have a distinctive collection of alleles, even if they can interbreed. In the last couple of years African  elephants were declared to be two different species even though there are existing hybrid populations.

Among other things this also means that the idea of speciation being macroevolution has died.