There are three ways to look at fighting (millions, of course, but three in this set) that are different, and those differences drive almost every aspect of the encounter. It's very clear, but sometimes people get confused and try to solve problems of one situation from another point of view. That fails.
I hate the word 'fight' because it implies a contest. 'Assault' doesn't work all the time as a word, nor does 'combat' so I'm going to default and use fight, but don't lock up on it.
Take the other guy out of the equation. There are three ways that you can go into a fight: You can go in on the offense, go in as a mutual fight, or be on the receiving end-- defensive.
Going offensive is not the same as being an aggressive boxer. It is a quantum difference. When you are intending to use force offensively, you have a goal. There is something or someone you want, some event that must happen. You do everything in your power to minimize risk. It is a job. Same as mining. You have a goal, you want to be safe.
So, offensively: you gather your intelligence, you choose time and place, you stack every factor you can control in your favor (weapons, armor, numbers, surprise) and you act, ideally never giving the victim a chance to respond in any way.
Good guys and bad guys do this. It is the essence of a military raid or a simple robbery. It is just the smartest, safest way to accomplish your mission.
So what skills do you need? Stealth. Clean hits. Almost any precision skill works here, very well. Emotionally there are differences, but whatever you train, if you have the complete drop, you can shoot like the range or strike like you were only hitting a bag.
Mutual fights have no surprise. Take that back- one of the essences of strategy is creating little pockets of surprise and some people go into a Monkey Dance believing the other guy won't really hit-- but generally, not only do you see these coming but both parties, on some level, have agreed.
They are very social. Consciously (sport) or subconsciously (Monkey Dance) they have rules. They almost always have an audience. Mutual fights are not about resources or survival, they are about communication: "I am a bigger monkey than you" "I deserve respect" "That's my woman" Stuff like that.
An aside- I like sport. Sports MA tend to be (IME) the least delusional of all martial artists (including RBSD) because they know exactly what they are doing and why. Most of us went into sports and competition to find out who we were and what we had.
In a lot of ways, mutual fighting is a testing ground and much of what it tests is attributional. Strength, speed, endurance, will. Many of which an offensive attack is designed to neutralize.
So what are the skills? You need the skills that you are testing. Boxers need boxing skills and judokas need judo. Then you need the attributes and then you need the ability to read an opponent and lead him and do all those things that add up to mat sense or tactical thinking.
A defensive fight is what happens when you are on the receiving end of an offensive fight. The bad guy has set everything up to his advantage. Whatever attributes you have trained (strength, speed, endurance) he has either found a way to neutralize or will simply (if he has the option) choose someone else. An unexpected blitz where your movement is restricted, probably coming from a zone where you have little practice or experience delivering power; with structure compromised...
What skills do you need here? The precision skills that work for an attacker won't be an option for you. If you can turn it into something that resembles a mutual fight, that's cool... but how? You can't handwave past that.
Most of the big chances to make things better come well before the attack. Use of terrain, reflections and shadows. Trying not to be surprised enough to ever be completely defensive. But that has limited utility, since these skills come into play when prevention skills have failed.
The skills I think are important? Having been inured to pain and the particular kind of chaos that comes with a blitz attack. Good training in a mutual combat-based system can help with that. Practice working against bigger, stronger people. Awareness and use of the environment and skill at exploiting momentum are probably two of the biggest. An indomitable will that goes to active rage instead of passive fear is critical, and I'm not sure if that one can truly be trained at all.
I see the lessons of these three as largely separate. Even though in any given assault one is offensive and the other defensive, the skills and strategies of the offensive actor wouldn't help the defensive. Nor will the defensive skill at recovery help the attacker. The type of tactical thinking needed in a mutual fight is counterproductive in both the offense and the defense. In the offense, it is unnecessary and the restraint required to balance offense and defense and feint actually impairs hard, efficient forward action. From a defensive position, trying to get 'set' trying to get into the position and distance where mutual fights start takes time and time is damage.
Some times I think I write the same things over and over in different ways.