The Fediverse is what you are on right now, it's a collection of lots of servers talking to each other. You and I are on different servers, but we are able to have this conversation because the servers are connected.
Most servers on the Fediverse run a piece of software called Mastodon, but some of them run other kinds of software.
However, all these different types of server communicate seamlessly with a common standard, so it ends up feeling like one network.