You are making sense, just remember your login does not travel between kbin and lemmy. When you are on kbin, you can search for communities on the server you joined or across the fediverse. The way to do that is community@instance.name
For example, say if I found out the beehaw.org server had an awesome gaming community, well I can just type gaming@beehaw.org into the search box and then subscribe to it. It will then federated into the server (the server will start pulling in new posts - but not old posts) that means others can now see it too. That's why if you see the message that it's not fully federated and you might see more on the original instance.
Your login is just a place to reside but with the fediverse, you can pull in content to view. Which helps as you don't need multiple log ins for multiple services. I've seen a few people ask about people with the same username as theirs on other instances and that will happen but remember that your username is like email. You have username@instance.name, so whilst someone might share the same username, they'll never be on the same instance. That's how you tell others apart.
Hopefully that helps make sense!
@Otome-chan@kbin.social yeah I've noticed that too, the trolls don't seem to be on kbin - kbin feels fresher and nicer in a way. Ernest has been doing a great job with this site