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.