I've looked this up before. "Goose" and "moose" originate from different sources, so their respective plural forms are different. "Goose" comes from Middle English while "moose" comes from an Algonquian language. I'm sure there's an article on the internet explaining this in more depth, but here are the Wiktionary articles on "goose" and "moose" - https://en.wiktionary.org/wiki/goose#Etymology and https://en.wiktionary.org/wiki/moose#Etymology_1
Copy-pasting my answer to the eternal elk question here:
"Is there an explanation regarding why two different animals, though similar, share the same name?"
If you need to differentiate, you can use "europeisk elg" for Alces alces, and "amerikansk elg" for Alces americanus. Of course you're only going to come across one of the two in Norway, so it makes sense to refer to it as just "elg".
The official Norwegian names for the wapiti, Cervus canadensis, are "wapiti" and "elk", but since this is an unfamiliar animal to most Norwegians, we'd probably go for "hjort" ((red) deer) if shown a picture and asked what animal it were.
Keep in mind that Alces alces is referred to as "elk" in Europe, so while you're interpreting the two accepted English translations of "elg" as a lack of nuance in Norwegian, it's actually a result of regional differences in English.
You can not use "are" for a single moose. The plural of "moose" is "moose", as explained in the other comments on this thread. The Norwegian "elgene" refers to the moose (or elk) in the plural. "Elk" can often mean the same the as "moose", and the plural of "elk" is also "elk". Other comments in this thread provide a good explanation of the differences in usage of "moose" and "elk".