#ActivityPub is super cool once you see it in action.
For instance, you can visit the new StarTrek lemmy server here: https://startrek.website/c/startrek. Looks like a reddit sub with posts, threaded comments, upvotes, &c.
OR you can follow the same server on Mastodon @startrek.
Every thread and comment shows up as a boosted post.
Cool, right? Now, say you find a comment that you want to reply to. Post through your favorite Mastodon app, and that feeds right back to the thread on the #Lemmy server! 🤯
startrek.website runs on lemmy, a reddit-like software on the fediverse (it uses the ActivityPub protocol).
lemmy.world and beehaw.org are examples of lemmy instances.
kbin is another (newer) reddit-like software that runs on the fediverse too.
kbin.social or fedia.io are examples of kbin instances.
lemmy and kbin differ in the details, they are totally different softwares written from the ground up to be like reddit but they are generally pretty similar in practice. Users on lemmy and kbin can follow, post and interact with each other as well as with users on mastodon etc… that’s what makes it federated!. Your login will only work with the website you made it at (here, at startrek.website) in the same way that your email login will only work at the website you have it setup at (i.e. gmail login won’t work for yahoo email).
Also, just to clarify, a particular website/community on the fediverse is referred to as an instance. startrek.website is a lemmy instance. Bit of a weird phrasing, but there are many different websites running lemmy software so a word had to be invented to refer to the various different websites running one version of a fediverse software (lemmy, mastodon, kbin etc…).
Sorry if that was too much of an explanation, I just figured there are probably a lot of new people here who might not quite understand how everything fits together!