The app and the website are not the same
“What is different in the iOS app?”
The app runs every Class Play game with no internet connection at all, which is its real advantage in a school with bad wifi. And from version 8.9.0 it can HOST live rooms too: tap GO LIVE on any game, students join at classbreak.app/join as usual, and your phone or iPad is the board. AirPlay it and it is the projector.
On app versions before 8.9.0, live rooms are website-only and the app is single-screen. Students always join from a browser: there is no student app to install, on any version.
A subscription bought in the app is managed by Apple and cancelled in your iPhone settings, not here.