The premise of your question is somewhat incorrect, though it's a common misconception by people conflating how Windows 3.1 worked and how Windows 95 worked.
In Windows 3.1, if an application had an error, it would show the graphical box you included, and as it says in the Raymond Chen article you linked that box sometimes had an option to Ignore the error.
You show the screen that one gets when hitting Ctrl+Alt+Del, but that's really just the Ctrl+Alt+Del screen. That's not an error screen, it's a tool used to help you stop a hung program.
There were some other "blue screen" messages, particularly for system messages that needed to coordinate between the DOS VMs and the Windows applications, such as handling device conflicts when more than one application was trying to use a serial port. You can see some examples in another Raymond Chen post, "Steve Ballmer did not write the text for the blue screen of death". These were messages not really specific to an application, but regarding sharing the system resources between them and prompting you how to handle them. However, as that article says, Windows 3.1 didn't really have a "blue screen of death":
If an MS-DOS application crashed, you got a blue screen message saying that the application crashed, but Windows kept running. If it was a device driver that crashed, then Windows 3.1 shut down the virtual machine that the device driver was running in. But if the device driver crashed the Windows virtual machine, then the entire virtual machine manager shut itself down, sometimes (but not always) printed a brief text message, and handed control back to MS-DOS. So you might say that it was a black screen of death.
To answer your question, the presentation of the message wasn't related to the severity, but whether it was an application-level or system-level message.