I'm not sure I grok the precise boundary you're drawing here.
It seems clear that (car 10) is always a bug, so I'm with you there. However, non-existent files may be bugs in some situations. Perhaps you're just proposing giving programmers two distinct labels to use with discretion? If so I shouldn't get hung up on precise examples.
A failure that is unexpected and unplanned for is a bug. Thus it's a bug if a file doesn't exist and my code doesn't handle that situation.
The boundary is what I want to happen in response to a bug vs. a failure. When I hit a bug, an actual bug, I want to capture the entire state and history of my program, to the fullest extent possible, so that I can find out why the bug occurred. I don't care if this a core dump is GBs in size or might be expensive to generate. If a bug occurs I want all possible information that might help me, everything that the language runtime can produce.
For failures, for expected failures, for failures I handle, I don't need to capture anything. I don't even need a stack trace. I don't need the language runtime to generate a stack trace every time I hit an expected, handled failure.
Existing languages don't allow me to do this. At the point where for example the "file not found" exception is being thrown there isn't enough information to tell whether that's a failure or a bug, so they have to be handled the same.