I believe "elk" is one of those words used differently on different sides of the Atlantic. What is called a moose in North America is called an elk in Europe. I don't know what a North American elk is called in Europe.
Wikipedia backs me up. It appears Cervus canadiensis (elk) went extinct in Europe in the Pleistocene. Alces alces (moose) is still there and known as elk (I expect alces is cognate with elk). Why Europeans in the New World adopted a local name for the familiar Alces alces and applied their familiar name to the unfamiliar Cervus canadiensis is a long story.