Distributed notification

A macOS distributed notification is a named message that software on the Mac can send to other software. An application can broadcast the message with an optional object and additional data. Other applications or processes can register to receive it. It is not a banner in Notification Center. Apple's DistributedNotificationCenter documentation

BetterDisplay can use these messages in two directions. Under Application Integration, it can listen for incoming integration requests. As a Control Integration action, it can send a notification to other software.

Configure the direction you need. Enabling BetterDisplay's listener does not create a receiver in another application, and sending a message does not prove that another process received or handled it.