There is a whole range of alternatives, several for microblogging (Misskey, Calckey, Pleroma, Akkoma, ...), some for macroblogging (Friendica, Hubzilla) and some that specialise in certain functions (e.g. Pixelfed for pictures, Bookwyrm for books, etc.).
Some short descriptions can be found here in the JoinFediverseWiki: https://joinfediverse.wiki/What_are_Fediverse_projects%3F
Its kind of both, it has its own centralized website, but also self-hosted instances. They were popular with web designers before social media took over the internet because they were easy to set up and super customizable.
Thank you for the graphic. Aretheree and fediverse sites you van personally recommend. I wanna get into social media but also I don't wanna sell my soul to Facebook or bytedance
It really comes down to what kind of social media you are looking for. Pleroma and Mastodon are people focused (i.e. you follow people, not topics), while Lemmy focuses on communities/topics. Kbin is somewhere in between, you can both create post on an individual timeline and in communities, but Kbin is still relatively new.
Personally, I like Lemmy most (though Kbin might become interesting in the future). The great thing about the fediverse is that you can post with your account anywhere (with some limitation between different services) so it does not matter if you are on lemmy.ml or feddit.de or beehaw.org.
As a nitpick about language and terms, I think it's important to recognize that Mastodon and Lemmy, Calckey, Friendica, Akkoma, kbin, PeerTube, PixelFed, etc. are not websites. They're different server types, which come with a web-based front end. These servers run thousands of websites, each of which is its own social networking site.
This is actually an important piece of how the Fediverse fundamentally works. Even if we're not using different server types (Lemmy, Mastodon, etc), we're still largely using different websites.
And while you can install an iFrame or whatnot in a website to serve content from other websites, that's generally not what happens here. Here, you view content on whatever website you've logged into. This means copies of posts are being sent all over the network, and are stored on and hosted from each site that receives them.
What you read is being served from the site you're using. When you post something, that post gets copied to other sites, and other people read those copies.
A common mental model I see people have in the microblogging corner of the Fediverse, following the Twitter migrations, is that "Mastodon" lives out there in a singular place, and people just access it from whatever website they registered on, like it's a mainframe and they're using a terminal to access it. But this is much more like a bunch of independent web forms (or blogs, in the microblog case) where people are actively cross-posting posts and replies, creating copies of discussions.