StS doesn't really have a story, but yes, it has characters instead; I don't really mind either direction, Balatro's fight-against-the-game is essentially the same thing.

They are different, and I do enjoy them both in their own ways. Balatro's heavy focus on combinations (and regular stores) means decks can shape quite quickly into something very unique. It's also more accessible as the games are shorter; StS can be an hour if successful, if not more. My comment is more that Balatro is newer and has at least satisfied the itch which - after being out for years - StS has perhaps not been able to do in such a way for a while.