I've been interested in strategy since early childhood, which led to game theory, which led to AI theory. AI theory is useful in general, and taught me that the best way to think about dimensionality is "degrees of freedom".
(Algorithms can think in n-dimensions, 800 dimensions as a example.)
One of the lovely things about the "sweet science" of boxing is that it has very few degrees of freedom—using the fists only to attack the brain or wind (body blows.)
Kick-boxing adds another dimension—striking with the legs and feet!
MMA adds two more dimensions—grappling and "ground & pound". (Leagues that allow elbow strikes add another dimension.)
Prize fighting & amateur fighting competitions also include a psychological dimension, which the best competitors utilize both in the ring and prior to the match.
An easy way to understand the distinction between sports and self-defense/combat is that the latter have many more degrees of freedom.
In real-world combat, there are no rules.
In real-world combat, weapons may be used.
In real-world combat, hard surfaces can be used as weapons.
In real-world combat, the combatants can often "choose their ground".
In real-world combat, surfaces can be irregular or slippery.
Military strategists have understood terrain and its utilization to be essential for millennia.
- In real-world combat, there may be lulls, but there are no water breaks.
Thus one must be prepared for continuous engagement of unlimited duration.
It's important that martial artists don't conflate martial sports with real world self-defense.
Training for and engaging in martial sports has utility in regard to self-defense, but they truly only cover a small number of the degrees of freedom of real world combat.
Training for martial sports is good for conditioning, and for getting used to physical contact, but too much can be detrimental, as it can result in injuries, which can inhibit capability and interrupt training.
(Taking too many blows to the head has been know to be detrimental, being "punchy" or "punch drunk", even before this was validated by empirical analysis.)
There is even an argument that training for sports competition is not ideal for real world combat because it limits the thinking, and potentially the training, to an insufficient number of dimensions.
- In combat, the concept of a fair fight does not apply.
From a self-defense perspective, "fair fights" can occur if, by chance, the opponents are equally matched. (The size, strength and skill differential can be a factor in what strategies a defender adopts. Attackers can be significantly less skilled than the target of violence, in which case the defender may opt to be gentle, but in situations where this is reversed, defenders have no choice to by inflict maximum harm by any means.)
Miyamoto Musashi is a good real world example, a duelist in the most lethal domain where a single mistake is fatal. In an honor/shame society, Musashi was willing to break convention as necessary in order to assure victory.
"Either you defeat your opponent or [they] defeat you. You cannot complain that [they] did not follow the rules. You have to overcome your opponent(s) in a way appropriate to each situation."
- Real world combat can involve multiple attackers.
Many schools train for this, but one of the potential problems of prizefighting at the highest level is it requires sole focus on single-opponent training.
Multiple opponent situations are the most dangerous for obvious reasons, so martial artists must be able to execute multi-opponent strategies without thought, and engage in some degree of training for this.
