Not what I meant.
On the home screen of Pokemon Sun or Moon if the game has an update installed it will list a game version.
The latest version is 1.2. Make sure both have the same version.
As for the Wi-Fi, the consoles don't have to connected to the internet if you want to have local play, they just need the Wi-Fi turned on.
The system will switch the mode to adhoc for local play if that's what you are trying to do.
GTS & WT can use local Wi-Fi. In your first post you said you are on 11.4 ( on at least on system )
This system can't connect to the Nintendo Network as you need 11.5 to do that ( in most cases )
I have to say it's most likely just a mismatch game version, disabled Wi-Fi or as
@Quantumcat said mismatched game or system region.
If this still doesn't work I'm out of ideas, Good Luck.