Coyote is considered a type of varmint.United States, Varmint & Predator Hunting:
Varmint hunting is an American phrase for the killing of non-game animals seen as pests. While not an efficient form of pest control, it does provide recreational hunting for hunters and is much less regulated.
Varmint species are often responsible for detrimental effects on crops, livestock, landscaping, infrastructure, and pets. Some animals may be utilized for fur or meat, but often no use is made of the carcass.
Which species are “varmints” depends on the circumstance and area. Common varmints include various rodents, coyotes, crows, foxes, feral cats, feral hogs, and groundhogs. Some animals once considered varmints are now protected.
Vermin:
Vermin is a term applied to various species regarded as pests or nuisances, and especially to those associated with the carrying of disease. Since the term is defined in relation to human activities, which species are included will vary from area to area and even person to person.
Disease-carrying rodents and insects are the usual case but the term is also applied to larger animals, on the basis that they exist out of balance with a desired environment, consuming excessive resources.
Predators:
Predator is an animal that hunts and kills other animals, usually for food, predation describes a biological interaction where a predator species kills and eats other organisms, known as prey.
Predators are either carnivores or omnivores. Usually treated separately is herbivory, which describes a relationship where a herbivore consumes plants. This may involve killing the organism, or eating only part of it (known as grazing).
However, from an ecological perspective, the activities of the herbivorous species that kill the organism they feed on is functionally the same as predation.
There may be hierarchies of predators; for example, though small birds prey on insects, they may in turn be prey for snakes, which may in turn be prey for hawks. A predator at the top of its food chain is called an apex predator.
Many predators specialize in hunting only one species of prey. Others are more opportunistic and will kill and eat almost anything. The specialists are usually particularly well suited to capturing their preferred prey.
There is a full spectrum of specialization. Some predators specialize in certain classes of prey, not just single species. Almost all will switch to other prey when the preferred target is extremely scarce.