My impression is that if you have an unhandleable error, for example an out of memory error, then it's best to quit immediately. Things are out of your control. That is a panic.
Many other panics show you have a bug in your code, for example, a divide by zero error, an out of bounds array access, in which case it's better to quit immediately with a panic. Then you know you have a bug to fix and where it is happening.
When thinking about errors it's useful to forget about the error free "happy path", think about all the error/failure paths, design your program to respond to them as you want. Those error paths deserve as much, perhaps more, attention in the design of your program than the job you actually want to do.
To your actual question. Consider opening a file for reading that does not exist. Something like fs::read_to_string() returns a Result which may contain an Error. That error maybe fatal, say it is trying to read a required configuration file, so perhaps best to check for that error, print a suitable message and exit the program. Not with a panic though. Or it might be recoverable, say the user typed a file name incorrectly, so you may want to prompt for a new file name and try again.