Pokemon Sun and Moon – Differences Between PokeBeans Colors

Serebii has a summary of all of the differences between the two versions.

In Pokemon Sun the first totem pokemon you encounter is Gumshoos whilst in Moon you encounter an aloan Raticate.

In Pokemon Sun you have the ability to meet and battle Kiawe whilst in Moon you can meet and battle Mallow.

You can also get different stores in the festival plaza. You can usually get them in both games to begin with but the higher level versions of them are only available in one version.

In the Battle Tree you have the ability to scout trainers. You can only scout Plumeria, Sina and Kiawe in Sun and you can only scout Guzma, Dexio, Malloww. As far as I know other characters can be scouted in both games.

source

Based on the page for Poké Pelago on Serebii, it looks like this is just to help random players over the Internet. It won't give you any benefit except the joy of knowing that you helped a stranger.

You can also, once a day, send out a Bean Bottle. This will put 7 of your standard beans out and distribute them across the Internet to other players and you will sometimes find Bean Bottles from other players turn up on your game.