What are the differences between system pop-ups and application message push?

The system pop-up is a pop-up box displayed by system in specific cases, for example, a system update prompt or a low battery prompt. System pop-ups cannot be proactively triggered or controlled by applications.
Application notifications refer to notifications sent by applications in the background and displayed in the notification panel on your phone or taskbar on your computer. For example, notifications about new messages on social media and new emails in the email application. You can choose whether to receive these notifications as required.