I don't think many loggers at all are afraid of their job or have many fears at all regarding it. Yes you have a statistically higher chance of dying while doing it than almost any other occupation but it isn't frightening. Yes, you might roll a skidder and get crushed. You might fell a tree and it knocks a snag loose and it brains you from 100 feet up. You might fell a tree and it gets hung up and falls on you. You might fell a tree and it might buck up off the ground kick back and crush you. You might walk out your front door and get struck by lightning or crash while driving to the grocery store. The majority of people who log for a living are aware of the possibilities but they look at it like any other way you can potentially die.
The tree isn't trying to kill you. It might kill you but shit happens. This is a fundamental difference to being a police officer where people ARE trying to kill you and WILL kill you if they have a chance. You might never encounter one in your entire career but that doesn't mean they don't exist and that you cannot be ready at any time for something to go down.
How different is it to logging in that regard? Being ready for anything at any time? I suppose it is similar but the difference is intent.
Like I said, I spent several years working as a logger. I was more nervous about wildlife(mind running wild, not legitimately concerned), both real and of the cryptozoological sort than I was of a tree smashing me and trees almost did smash me several times. I obviously can't speak for everyone who has been a logger. I was never afraid that a tree might kill me in a general way. Yes there were times when it was windy and falling was a bad idea. Or a tree was clearly hung up with another. Those were squeeky bum moments but the fear in those situations was proportionate to the threat. I could see the threat, I could anticipate it. I knew at that moment I was risking my life.
Police don't have this luxury. They cannot identify the safe moments from the danger moments. When they are out and about they always have to be on high-alert. That is what is psychologically draining and taxing.