Players have to manage a “vault” where survivors live their lives underground. It was a success, so Bethesda soon released the game onto other platforms like consoles. In case you don’t know, Fallout Shelter is a game from Bethesda based on the Fallout franchise.
There are some advantages or perks if you download it from Steam of course, like Steam achievements and Steam’s cloud support, but aside from that there’s no real difference. Whether you get it from Steam or any other platform, it plays the same, but some gamers might prefer keeping all their games in one place on Steam.