Most people in Europe do not use English as their everyday language, and those who do have neither Alces alces nor Cervus canandensis at hand to look at. Which is probably why they got it wrong and applied the word "elk" to the wrong animal once they got across the pond. They should have asked some Scandinavians. :-)

Based on the comments and the Naming and Etymology section in the Elk wikipedia. I think in Europe the term "elk" refers to both elk and moose.

"European explorers in North America...thought that the larger North American animal resembled a moose, and consequently gave it the name elk, which is the common European name for moose"

Elk in the UK are referred to as red deer, though recent taxonomy has decided they are a different, albeit closely related, species. I don't know what they're called in other languages.

https://en.wikipedia.org/wiki/Red_deer

The Norwegian Wikipedia article calls our "elg" for Alces alces, while saying the larger American moose is considered a sub-species Alces americanus.

[1]: https://no.wikipedia.org/wiki/Elg

> If Europe refers to moose as elk, what do they call elk?

I believe the answer is they don't have an American Elk equivalent.