The dog and the wolf are actually the same species. Their physical appearance is similar but their instincts, disposition and temperament vary widely.
The gray wolf, or simply the wolf is the largest wild member of the Canidae family. The dog is the domesticated form of the gray wolf. Genetic drift studies and DNA sequencing confirm that domestic dog shares a common ancestry with the gray wolf. Eurasia and North America used to hold most of the world’s wolf population but the numbers have begun to dwindle due to human encroachment. Dogs are commonly seen in any place that is inhabited by people.
Dogs have relatively smaller skulls with varying muzzles, physically smaller brains, smaller teeth and varying leg lengths as compared to wolves. Smaller brains require less calories for dogs to survive. The paw of a dog is half the size of that of a wolf, and some dog's tails curl upwards, unlike that of a wolf. Dog teeth have less complicated cusp patterns and a much smaller tympanic bulla as compared to wolves.
Wolves have larger, broader skulls with a longer muzzle, physically larger brains, larger teeth and legs. They have a narrow chest with forelegs pressed into it. Elbows point inwards and feet point outwards. Also, wolves have a pre-caudal gland at the base of their tail used to release a pheromone onto another wolf, marking that wolf as a member of a particular pack. This gland is vestigial in dogs and functions only minimally in dogs.
Dogs are descended from wolves and are the first animals we humans domesticated. Tens of thousands of years ago, humans domesticated wolves and these tamer wolves evolved into dogs. There is some evidence that this domestication happened more than once:
[When we domesticated the wolves, they...] changed in body and temperament. Their skulls, teeth, and paws shrank. Their ears flopped. They gained a docile disposition, becoming both less frightening and less fearful. They learned to read the complex expressions that ripple across human faces. They turned into dogs. Dogs were the first domesticated animals, and their barks heralded the Anthropocene. We raised puppies well before we raised kittens or chickens; before we herded cows, goats, pigs, and sheep; before we planted rice, wheat, barley, and corn; before we remade the world.
Dogs have been domesticated for a very long time now, and understandably more responsive to domesticating techniques than wolves. Dogs respond to the voice; wolves to hand signals. The dog has lost some of its hunting ability because of domestication. But dogs can often read facial expressions of their human masters.
The wolf is a natural hunter. Wolf teeth are designed for hunting. Wolves have stronger molars than dogs, enabling them to crush large bones. Wolves could prey on little children. Dogs, on the other hand, are very friendly and playful towards children. Feral dogs have been known to kill small children and attack adults.
According to National Geographic's award-winning show, Dog Whisperer with Cesar Millan, humans need to dominate their pet dogs to get them to behave. The logic was that dogs are descended from wolves, and wolves live in hierarchical packs in which the aggressive alpha male rules over everyone else. However, many experts say Millan's philosophy is based on now-debunked animal studies and that some of his techniques - most famously the alpha roll, in which he pins a dog on its back and holds it by the throat - are downright cruel.
Experts also suggest that wolves live in nuclear families where the male wolf is like the father and other wolves following the leader of the pack are like children following the lead of their parents.
Most domestic dogs are sexually mature by the age of 6 to 12 months (some large breeds take slightly longer). Wolves reach sexual maturity after two or three years; that's when they leave their pack in search of a mate. Female wolves come into season or heat only once in a year, while domesticated female dogs heat two times a year. Only the alpha female wolf is allowed to breed. There is no such hierarchy or difference amongst dogs.
Wolves are social and live in packs. They need fenced yards and constant monitoring. Dogs generally live by themselves, and most need no containment. Wolves are generally more intelligent and more aware of their environment as compared to dogs. But when it comes to sociability, dogs are generally more sociable with animals and sometimes with other pets as well. It is almost impossible to house train a wolf. Dogs, because they're domesticated, can be trained with relative ease to follow commands and perform various tricks.
Although dogs fall under the category of carnivore, they are largely omnivores and can digest a wide variety of foods like vegetables, grains, fruits, plants and meat. Wolves primarily feed off meat and even fish, and attack medium to large sized ungulates with their hunting prowess.