"Man, I'm hungry. What do I have left? Let's see... cold rice, soy sauce, a few small chunks of fish from yesterday and there's some seaweed growing in the fish tank? There has to be a way to turn this into something!"
In Japan, sushi is definitely one of the more expensive foods. You can't really use yesterday's fish as authentic sushi uses fresh fish which you can't eat the next day for obvious reasons.
People started putting all kinds of fillings into sushi like chicken, beef, sausages, vegetables and whatnot. So... fresh fish ain't a requisite for sushi anymore.
Isn't that kimbap? I think sushi is raw fish or sashimi when using raw meat. And the Korean kimbap uses cooked meats. I could be wrong, but I think those are the differences.