Deer, Elk, and Moose are all part of the Cervid or deer family.

Also, in various parts of the world, the names are commonly used for different specific animals, which can be confusing. What's called a Moose in say, Sweden is called an Elk in Britain. But what we call elk in the US are a different species entirely. Elk in the US are another name for the red deer species, which was once considered merely a subspecies.