In iOS, a "Local Notification" is used by an app when it is in the background, to inform the user that something has happened, that they might want to pay attention to:

Local notifications ... to inform users when new data becomes available for your app, even when your app is not running in the foreground. For example, a messaging app might let the user know when a new message has arrived, and a calendar app might inform the user of an upcoming appointment.

Apple dev - Local and Remote Notifications Overview

[Its "local" if the app itself is providing the new data; "remote" if a remote server is sending the update.]

Is there an equivalent on Android?

android notifications local
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