Spitting into the wind at this point, I know, but it still bothers me.
Now consider Mastodon as an email client which is hosted on a web site, like Gmail or Yahoo! Mail or Hotmail. That web site gives you an interface with which to interact with the network of email servers, but people using other servers with other interfaces can still see messages from each other; someone using Yahoo! Mail can send and receive messages with someone using Gmail.
The difference is that Mastodon is open source, so that anyone can download the code and run their own Mastodon instance (whereas nobody can download and run their own Gmail instance), but that instance can still exchange messages with instances running any of the several other Fediverse interfaces there are out there, such as Pleroma, Misskey, Soapbox, etc. (Unless an instance at either end has "defederated" the other; that is, the administrators have configured it to not exchange messages with the other server.)