so what is the difference?

The scheme (sometimes called "protocol") is part of the origin of the page. Every distinct origin gets its own store, isolated from the stores for other origins. Since http://example.com and https://example.com are different origins, their stores are isolated from each other just as much as the ones for https://a.com and https://b.com.

The functionality of the stores is the same, it's just they have different contents, because they're for different origins.