The short answer is that moose were called elk in England but they have been extinct for close to A Thousand Years. Despite this the name had remained as the name of that animal over there which people thought of as a big deer. When English speaking people arrived in Canada / North America they encountered a number of species that were unfamiliar to them, such as what we now call caribou and Elk as well as deer and moose. People actually adopted a few indigenous names into English such as Wapiti for some of these species before settling on the way we use our words today with elk being used for the large deer species and moose being used for what long ago was called an elk in England and Caribou being used for what used to be called reindeer in England or at least by the English. This follows a fairly similar pattern to a lot of name changes. For example an American robin is not the same as a British Robin, the names of weasels are not always the same, different fish bear the names that were familiar from Old World fish and so on.

I have done a lot of work with old archival documents connecting documented bird names to actual bird species and the number of times you have a sparrow called a swallow or some bird given the name have a bird that only lives 5,000 miles away is very high. The same was true of fish where local names in English we're completely different from the names I might be able to find on the internet and it took a good deal of asking old people questions to actually determine what these phrases meant and only then being able to connect a document and description of a fish with a specific species and then connect that species to an indigenous name. Sometimes physical descriptions and descriptions of behavior were the only thing that allowed me to identify a bird as the name was absolutely useless.