Whenever I tell people that Mastodon isn't the Fediverse, the Mastodon stans start saying, "Oh, you sound like a guy who's complains that Linux isn't called GNU/Linux."
No, there's a massive difference.
To most people, whether you call something Linux or GNU/Linux doesn't affect the user experience of using the OS.
Referring to the Fediverse as "Mastodon" definitely affects the user experience of using Mastodon.
If Mastodon users don't know about the Fediverse, they don't know why the messages they receive look wonky sometimes.
"Why is this guy allowed to post with more than 500 characters?" they often wonder.
"Why are there links in this post? Why can't I see things that other people can?" they'll ask.
And then they realize, "Hey, that guy can quote post! I thought Mastodon didn't allow that! How is that possible?"
Well, yeah, because those deviations require the context of the Fediverse.