In case the email analogy doesn't work for you, let me let me try to explain. You're on kbin, you can tell because your username ends in @kbin.social, which is a kbin instance. Instance is just another name for a server. Due to federation you can view and comment on threads from any other federated instance. You can also join maganzines (called communities on Lemmy, groups on mastadon, and subreddits on reddit) from any other federated instance as well. The only thing I don't think you can do is become a moderator on another instance. Note, the content is being brought to your kbin feed because we are federated, if you go to to the original instance you've left the website and thus won't be logged in. There's nothing to stop you from making another account with a Lemmy instance, but there's not really any reason to because you can see the same content.
Catch42