Japanese Language: Sake vs Salmon

In Japanese food, you can often find salmon used in different ways. Sushi, of course, is a very popular usage of this fish, but they are also often grilled and served with rice.

What I find very interesting is that for sushi, people often use the English word "salmon", but they use the Japanese word "sake" 鮭 if the salmon was cooked.

This onigiri, for example, contains sake. However, if you find raw salmon, it will contain "salmon" instead, despite both being the same fish.

I find this rather weird and really question why it is.