In the context of geezer's post that I was responding to, I took "fighter" to refer to someone who has tested their combative skills in some sort of hard contact rough-and-tumble environment. That could be someone like a LEO or bouncer, someone who has gotten into a significant number of street altercations, or a competitor in some form of full-contact martial sport, like MMA, boxing, or kickboxing.
I'd say it's really more of a spectrum than a strictly binary classification. I consider myself to be more "fighter-adjacent" then a full-fledged fighter. I've been in a few street altercations, I've fought a couple of amateur kickboxing matches in the ring. I've done some grappling competitions. I've participated in a significant number of SCA heavy weapons tournaments. That experience gives me a leg up on martial artists who have never done more than cooperative drills, but it pales in comparison to some of my training partners who have had dozens of professional fights or decades of LEO experience.