it's a bit of a mess, they have different features and share the baseline functionality.
The first one you listed (related-posts) is the one that gets all the features, even experimental. It offers automatic related posts, manual related posts and manual in-text links.
So if you want to test the most full-featured version, that's the one to check. You should expect features that are just experimental and they sometimes break. It's a bit of a test bed. I think we need to document that in the description more explicitly.
The stable one is WordPress Related Posts. It doesn't have all the features, but it should be rock stable. Right now it doesn't have manual in-text links. The middle one you mentioned is an experiment of its own - we wanted to put much more emphasis on statistics via opt-in registration and experiment with that. But didn't really get to it yet. So we just added the stable manual related articles lately.
Thank you for asking. We have to do a better job of explaining the differences.