Everyone needs to know there's a Fediverse -- much like they need to know there's an Internet.
Referring to @pixelfed as a Mastodon app, for example, is kind of like referring to Wikipedia as a Facebook app. Yes, @pixelfed interoperates with Mastodon, but it's not a Mastodon app. Yes, Wikipedia connects to Facebook via hyperlinking and previewing, but it's not a Facebook app.
You wouldn't refer to Facebook as the Internet. This is why you shouldn't refer to Mastodon as the Fediverse.
@pixelfed I've had a number of people say to me, "Mastodon is a synonym for the Fediverse."
That's only true if you never leave Mastodon, and believe other services work exactly like Mastodon.
For example, look at this feed. If I showed this to a complete noob and said, "This is Mastodon", they would be completely confused.
And that's because it's actually not Mastodon in any logical or meaningful sense.