Think about email in comparison to for example Facebook. On Facebook, the content and the platform are to sides of the same coin: the two cannot be separated. In email, on the other hand, the two are separate: the content (emails) is separate from the provider (Google, Protonmail, or some old laptop with an internet connection functioning as a server). Emails can be sent between the different platforms, as it is based on a protocol that exists independently of the providers.
Lemmy is the same way. In the example above, Lemmy is a piece of software you could install on your old laptop (or other people can install on hopefully more sophisticated servers) in order to communicate with other services. That's why Lemmy can be found on multiple websites (lemmy.world or beehaw.org, among others). Just like in email however, the protocol is separate: the protocol Lemmy runs on is called ActivityPub, and works with not only Lemmy, but also other software. Mastodon is the most famous; kbin is another.
Like Lemmy, kbin is a client for ActivityPub that is made to function a lot like Reddit. It is developed completely separately, but according to similar logics: I saw your message in kbin and am responding to it from there, and when I upvoted your post you recieved an upvote in your Lemmy. It's similar to if you are using Outlook and I am using Gmail: I can still send you an email and communicate effortlessly across the two services.
The difference between kbin and Lemmy is mostly in user experience. Both projects are work in progress, development is happening fast, and they have both seen an explosion in the number of users the last few days. Content spreads between both freely, so the choice between them is really mostly about user interface preferences. It will be fun to see how both projects develop.