Lemmy is a software package set up to create a Reddit-like experience on the Fediverse.

At about the same time, there was a similar software package that was compatible that was written called Kbin. While the author---who IIRC was doing this for a university project---didn't want to continue, it was open-source, and other developers continued it as Mbin. It has some other features, notably including support for Mastodon (the Fediverse's Twitter analog)-style microblogging.

After these two, there was a third software package that was written, Piefed.

All three are intercompatible, and one can choose a home instance that runs any of them, sort of the same way that there are different email server or Usenet or Internet Relay Chat servers that can all speak the same protocol and talk to each other.

They have different-looking Web UIs and different feature sets.

Your home instance is lemmy.world, which runs Lemmy. It's the largest Lemmy instance.

The largest Piefed instance is piefed.social.

Fedia.io is the largest Mbin instance (though they turned off anonymous access a while back to help keep load from scraper-bots down, so one has to create an account to try it out).

And then there are various native clients with support for various of these. I use Eternity when I'm on Android talking to Lemmy (it is, unfortunately, not being maintained, but it's presently my favorite there). Interstellar works with all three of Lemmy, Mbin, and Piefed.

Additionally, Lemmy has various alternate Web UI frontends that various people have created; these use the underlying Lemmy server, but look quite different. Some home instances run multiple of these for their users. Your home instance, lemmy.world, does this with several:

• a.lemmy.world: Alexandrite

• photon.lemmy.world: Photon

• m.lemmy.world: Voyager: optimized for mobile web browsers

• old.lemmy.world: mlmym, a clone of the old.reddit.com Web UI

• blorp.lemmy.world: Blorp