“Buck” and “stag” refer to the same animal, with the only difference being the size of the animal. All male deer are referred to as bucks, but a large male deer is sometimes referred to as a stag.
Deer are a member of the Cervidae family, which includes elk, moose, reindeer, white-tailed deer, black-tailed deer, and red deer. They are ruminant herd mammals present on every continent except Antarctica and Australia. The terminology for male and female deer varies widely and is sometimes determined not by species, but by size. For most types of deer, males are called bucks and females does. A stag is simply a large male deer; however, this term is not universally used. Some larger species are referred to as bulls for males and cows for females.
Deer terms can also vary for different age groups and occasionally by species. A male red deer is a hart and a female red deer is a hind. Again, these terms are not standardized and apply especially in cases when the male is more than 5 years old and the female more than 3 years old. Hart and hind can also be used to refer to species of deer other than red deer. A long time ago, the word “deer” was fairly generic as well; in Middle English it referred to any species of wild animal, while “cattle” referred to any species of domesticated animal used for livestock. It was not until much later that the word “deer” came to designate the Cervidae animal with which it is now associated.