Lemmy, piefed, and mbin are all similar pieces of software that run on a server.

They are each capable of hosting a small social network with a similar reddit-like format. They all also support the activity pub standard, which means that they can be linked together, so that when you go to one of those social media sites (lemmy.world for example) you can see any other site that they’re “federated” with, even if that social media site is powered by a different software that supports activitypub (I’m on lemmy.world but I can see communities and posts from piefed.social)

I generally call lemmy, mbin and piefed “fediverse platforms” because they’re each a platform that you can make a fediverse account on, but that usage is a bit imperfect, since each individual site could also be described as a platform, and is where your account is actually hosted. You could be more specific and call them “fediverse/federated link aggregators” if you wanted to specifically refer to the ones with a similar format to reddit.

They’re different because different pieces of software are built in different ways (different languages and underlying structure), have different priorities, and as software projects are run in different ways with different leadership, all of which is how you get differences in features and implementation. Lemmy is the oldest of these similar platforms, and as such is the most established. In the open source world it’s very easy and common to end up with a lot of fragmented similar projects. Its both a blessing and a curse.

There isn’t perfect language for all these things because in the grand scheme of things, it’s a rather new way for social media platforms to work, so the language around how to describe or refer to these things hasn’t really “settled”