You can play the Arcade version on an iPhone and iPad because the game data is saved to your Game Center ID. This means you can pick up where you left off on one device after you close it, and continue playing the save file on the other device. On some Arcade games, you can even play them on your Mac and Apple TV, but for Stardew Valley+, the compatibility shown in the App Store description only mentions iPhone and iPad (and iPod).
If you want to play between your iPhone and iPad, make sure your Game Center ID is the same on both devices. It defaults to your device's Apple ID but some users prefer to have a separate Game Center ID, so that's why I mention making sure you're logged into Game Center with the same ID.
Have fun!