The first is for those who want to compete to the fullest. The second is for those who want the Slay the Spire experience, but don't have a lot of time. The third is for social interaction and multiplayer experience with the current game systems.
Yano emphasized that he is not sure if all modes will make it into the final version. He doesn't want to create a lot of modes for the sake of quantity:
If we know that only two of them are interesting, I just hate the idea of 23 useless buttons on the screen. For me, that's a definite "no."
Slay the Spire 2 was released a month ago, and the developers are planning a long early access period.