Whether it's a crash or not is independent of whether you even haven a monitoring system, an operations staff, or even if you run the program as a service or not.
Heck, your monitoring system could still notice the program exiting and call your operations stuff in Rust's case too.
And a user with sudo rights killing -9 a program you run might or might not send anything to your monitoring system -- but that wont be a crash either.
I think the important point the parent is trying to make is between a crash and a controlled exit, that is whether you get a stacktrace, things can be called to cleanup, etc.
Merely calling all the cases just "crash" would lose that distinction. It's like calling all vehicles "vehicles". Sure, it's accurate, but I want to know if it was a car, a motorcycle, a truck or whatever.