How it works in the fediverse in general is that you log into your home instance and navigate to the other instances from your home instance. You won’t be able to log in with your Lemmy.world credentials on lemmy.ml. You can, however, view lemmy.ml content and interact with it (same for kbin.social) in the same way that I’m talking to you from a Lemmy instance.
kbin and Lemmy are two different ActivityPub softwares with similar goals and so you can use them interchangeably. If you prefer being on kbin.social and you prefer the things kbin as a backend provides to you more than lemmy, then you can use kbin entirely and still interact with everyone else. That’s the magic of the fediverse. Think Gmail vs Outlook. It’s still emails. Just flavoured differently.
This would make great copypasta