Pokémon sun – locked out of 3rd island. Cannot progress forward

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

If your guest list is full, your friend will automatically be kicked out (disappear). The only way to fix this seems to be adding them to VIP lists which guarantees they'll be there every time you enter Festival Plaza.

However, this assumes that you're already able to see them - to make them appear for the first time you'll just have to refresh your guest list until they appear. To force a re-sync of the guest list, I'd recommend both parties to disconnect and reconnect to the Festival Plaza.

Source: Reddit & personal experience