Differences between the three Ask to Join Networks settings in iOS 13?

What I commented above was almost correct.

the popover was very annoying to see when Wi-Fi is on and I am away from known networks. So maybe a notification comes when there's none. So that I can finish what I was doing and then try to connect to something.

The excerpt from an article:

Off ( This requires you t manually select a network if no known networks are available)

Notify ( Known networks are joined automatically. If no known networks are available you will see a notification for available networks)

Ask ( Known networks are joined automatically. if no known networks are available you will be ‘asked’ before joining a new network.

From https://appletoolbox.com/wi-fi-issues-after-updating-to-ios-13-or-ipados-check-these-10-tips/

The difference seems to be in the direct popup with list of networks vs the notification about available networks which won't interrupt your work.