I'm a little lost myself, so take this with a grain of salt, but....
kbin has more complete microblogging integration. I don't understand what it looks like or feels like, but here on Lemmy, I believe you can only post URLs-to and screenshots-of Mastodon posts. Not the posts themselves.
The ActivityPub protocol underneath Mastodon and Lemmy technically supports that kind of interoperability. That's why Mastodon users can comment on Lemmy posts and on Lemmy comments. But Lemmy has not yet adopted that feature. As far as I know.
Which makes kbin a combination twitter/reddit. And it makes Lemmy a "reddit, but twitter users can find our posts and comment on them using their Twitter account in such a way so that they're visible even to us Lemmy users, and boost our comments and posts to their followers."
They're different programs that do the same thing and communicate with the same protocol. Some servers run Lemmy, others run kbin. They have slightly different featuresets (afaik kbin integrates some microblogging functionality in addition to threaded comments and link aggregation) but it's really a matter of preference.