Not quite.

Mastodon is part of the Fediverse, a federated connected 'universe' of network sites that link to each other. Individual sites are hosted on the "instances" (aka servers). An individual belongs to a server that serves "twitter" like experience, it can even "look like" Tweetdeck but in reality is it more like an email.

In masotodon, people are assigned an identity that goes like `@identity@server` and everyone is identified by that identity rather than a common username. Besides, while Mastodon is specialised to share "status updates", there are other instances that can host other federated services such as pixelfed (an Instagram like service for sharing photos), or Peertube (a Youtube like service), or Funkwhale (a Spotify like social music sharing) or Bookwyrm (think of it like Goodreads) or lemmy (like Reddit, link sharing and commenting). The beauty of this ecosystem is that you can read all your posts everywhere on the Fediverse from a single account in the server. You will of course, be on different servers to learn about them, but the network is complex and interesting so that you can find users based on your interest.

So, Mastodon is just one app.

With Musk buying twitter, people have joined not just Mastodon, but ALSO other services. I believe for the record, these need to be accounted for as well.