An irregular reminder that calling this place "Mastodon" has a bit similar energy as saying "I just sent you a GMail."
"Fediverse" (or "fedi") is a better term.
Mastodon is just one of many software projects that talk to each other to create this multi-instance social network:
https://axbom.com/fediverse/
(kudos to @axbom for this fantastic infographic!)
There are blogs, Reddit-like communities, video instances and many more, all part of fedi.
I edited this toot, as there were too many people pointing out it sounded "annoyed" or "scolding." That was never the intention, and I am sorry it came off that way to some of you. 
That said, I do believe language matters a great deal: "The limits of my language mean the limits of my world."
I am not trying to convince you to always use one term over the other (I too sometimes use "Mastodon" in that context). Okay, maybe a tiny bit.
But mainly, I am trying to give broader context.
I have also seen a lot of people saying "well the app is called Mastodon" — sure, but there are a lot of other apps you can use. Tusky, Metatext, Fedilab and literally dozens more:
https://www.androidauthority.com/best-mastodon-apps-android-1210889/
https://transponderings.blog/2022/05/21/eight-mastodon-apps-for-iphone/
If you happened to download "Fedilab" first, would you argue the whole network is called "Fedilab"?..
And being aware that there's a broad spectrum of options might help you find a mobile app that maybe even works better than the official one. 
There's one more source of confusion here: the app-to-instance API.
Everyinstance uses Activitypub server-to-server to talk to other instances. On the client(app)-to-instance side the story is more complicated:
Many instances use "Mastodon API" to let apps(clients) talk to it. This is (IMO sadly) the default.
There's an ActivityPub client-to-server API. It's very rarely supported (in particular, Mastodon doesn't support it, but Pleroma does). That API is slightly underspecified (attachments, authentication), so usually it's used in combination with Mastodon API.
