It's kinda true - profesional chefs get more small burns on their arms and hands than many other occupations. And that is a fairly accurate way to identify a fulltime cook. But these specific pics are more the signs of too-busy, overworked, hungover, tired chefs rather than the norm.
For me, burns on the forearms were the most common from reaching into very hot ovens, they are tolerable and I could work through the pain without impacting the quality of my work too much. But hand and finger burns really lower your dexterity and fine motor skills and most cooks will avoid that and protect their hands as much as possible. Unless they are a sado masochist.
The guy with the giant blister on his palm looks like he picked up a hot pan with a wet towel (or perhaps no towel at all). Very common spot for a pan handle burn and a very amateur move. I've burnt myself like that and my head chef bollocked me for it because now I can't do half of my assigned tasks without wincing or spouting blister juice everywhere and everyone else has to pick up the slack that my burnt-ass-hand created.
The guy with the burns all up and down his arm looks like an exaggerated version of what a chef's arms usually look like. But even then, dude, are you self harming? Are you overworked? Maybe you should have got more than two hours sleep before a 12 hour shift. Honestly the nights in which I got the most burns were nights when I got fucked up on drugs and booze the night before. No one to blame but myself.
But yeah, this meme looks like it was made by a guy with an onion tattoo on his neck with less than two years experience. (There you go, some bonus gatekeeping in comment form)