I may have gone a bit into the weeds with the some possible causes, but nearly each point has a distinct difference that can be seen. Sure, the user may look at a website/browser error and not have any idea what it means, but it doesn't mean they can't relay the message.

For example, "The website is down" vs "When I go to the website, I see the message 'This site can't be reached. some-invalid-website.com's server IP address could not be found.'"