Unlike many of these comments, I've never had a "blank" experience or the caveman rage, except maybe as a small child.
I've negotiated my way out of fights where the other man was that angry (e.g. over romantic jealousy). I've always tried my best not to engage someone who's fighting out of blind rage and, to date, I've never had to. I had one guy holding me by the shirt collar with an arm stretched back to throw a punch, and I stopped him with a few words at that point. He wanted a fight, over this girl, but he realized that hitting me wasn't gonna get her back. He wasn't gonna look tough for beating me - I was gonna look magnanimous for taking a few licks without putting up. He ran away and got picked up by the cops.
I fought back against bullies a few times; and I've fought for fun with friends both in and out of a ring, and with and without pads and gloves. None of those were dangerous, and everyone I've fought like that was already or became a friend.
I was also really into martial arts as sport. I did years of kickboxing, some mma, and I've dabbled in a half-dozen more stylized martial arts, like kung fu, just to try them on for a year or two. I've lost many sparring bouts.
I've never lost a fight, because I've never engaged in a fight that I was likely to lose. I've run away from fights and I've avoided situations that were likely to cause them. I just don't put enough ego in appearances to get thrown off by someone talking shit, and I don't talk much shit either.
Anyway - a real fight is fast. Really really fast. What you see in the movies isn't worth anything. Most fights are over faster than Rousey's matches if anyone knows what they're doing. Winning a fight means being quick, using what's around, and being aware. I was in a fight where he put me in a full choke, and I won by doing a somersault into some heavy furniture. He was dislodged and pretty shaky getting up. I won another fight by being aggressive. He was stronger and bigger than me, but I spent all my energy in a few seconds to pop him in the face and it made him believe he was gonna get embarrassed. In a fight where someone wants to hurt you, you use all your strength as quickly as you can to win.
Anyway, this is how training affects fighting.
Untrained dudes sometimes do a lot of posturing and big, slow movements. They go for the face without considering how much closer the knees are. They punch for the face when they should lead with a push-kick to the gut. Those fights are emotional.
I've never had a fight like that. When I'm in a fight, I think about which leg their weight is on. I think about how much space I have behind me, whether my shoes are good for a dash or not (or if they're flip flops), and whether anything I have in reach could be thrown at their face while I rush. I always (granted, fights are rare for me) go for the same two takedowns, because they're comfortable to me and I'm used to them. So in a sense it's pretty formulaic.
I close while blocking my face, push (usually a push-kick to the leg or abdomen) to get them off balance, grab, and move them to put all their weight on one leg, and then I knock it out from under them with my hip or my leg. This throw is the kind of takedown that they teach marines and police officers. It's taught in Judo. I don't have the experience to control it very well, and I'm not subject to the same standards as officers when defending myself, so I throw as hard as I can and hope the landing hurts.
The other takedown is harder to describe, but I use it when I get rushed, and it's decent. Both came from MMA.
That's usually it, but it's also not hard to get a simple arm-bar after for some extra security. Again, this is all super fast.