Reddit Migration

Kbin is different code, and Lemmy is different code. Whatever instance you're on, if you made an account with a Lemmy-based instance then you login to Lemmy and thus use a Lemmy oriented app. Same for Kbin. If you use an instance that's using Kbin code (I know there are others but I'm only aware of kbin.social right now) then you login to it using a Kbin oriented app.

As for the content, it's all federated and if it works properly then you should be able to see Lemmy and Kbin content regardless of what app you're using, with the exception of content from defederated instances (regardless of whether they use Lemmy or Kbin). The sharing of content happens using ActivityPub which, while external of both Lemmy and KBin, are used by both (and many others like Mastodon) for the federation thing to actually take place.

In practice you wouldn't have to worry about it, except for choosing what app to use and whenever you're searching for communities on other instances (which on kbin search is something like "community_name@instance.name"). That's how I understand it at least.