Mastodon apps for Android: Tusky, Fedilab
Mastodon apps for iOS: Toot!, Mast, Amaroq
There is no app called “Mastodon” because anyone can develop an app (and the aforementioned ones are made by independent developers). You can also use the website on your phone, it works quite well and has 100% of the features.
For a more complete list of apps see https://joinmastodon.org/apps
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!