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