What should you do in both cases? You may first restart your laptop to see what happens. But others may be bothered by the ASUS laptop screen black but computer on. You may find your laptop is not booting when seeing ASUS black screen.
Unknown hardware or system issues are detected on the laptop.The laptop is overheating, so the display is turned off it's possible that only the power to the GPU is cutting off.Peripheral devices connecting to the laptop are causing the issue.
You can find your ASUS laptop black screen with cursor/on startup/after login/after sleep/after an update or when the fan is still running.