Are Martial Arts, Combat Sports and Self Defense different?
In short, tl;dr ... yes.
Being proficient in one does not automatically put a practitioner in a place to teach the other. Not even a little bit. One could almost argue the opposite.
I will begin this tirade at traditional martial arts (TMA, for the purpose of brevity). Not to be discounted as their merits are plenty, but TMA are generally antiquated forms of combat from all over the globe, but generally following relatively common lineages or situational development. Just the same as i wouldn't purchase a horse and buggy or a camel to help me conquer the hurdles of urban transportation, as much as they would get the job done it is incredibly unrealistic to expect it to be a practical solution to a contemporary problem in modern day urban city North America. Small sects of people (they aren't reading this unless they are on Rumschpringe, and in that case they would probably agree) are able to make it all work for them, but in such cases it is less that they are using antiquated forms of transport, but living an antiquated way of life.
People still raise horses. They still have wagons and carts and buggies. Its all a part of our cultural heritage. I even know a man with an entire herd of white camels. By and large it is an exercise of doing, for the love of doing so. That doesn't take anything away from the love of doing it, in my opinion being able to accept it at face value makes it more useful.
A wrench can be used to bash something but that doesn't make it a hammer. Calling it one and trying to convince others that it is, in order to validate your actions might make you a bit of a huckster. Blindly believing it is when you have clear evidence that it is indeed a wrench, makes you more of a halfwit.
I've spent countless hundreds and thousands of hours in training halls, gyms, dojos and arenas learning TMA. Was it a waste of time? Had I not taken the time to do what I have done ion these settings, I wouldn't be who I am today. I like that guy. He took alot of work to build (not find, build). The tenacity required to show up regardless of all of the other things you might want to do because as much as you've put in time to get where you've gotten (and how much more to get where you are going), your teachers have put the same amount of instructional time into you. Value that relationship as it is built on a few very fundamental truths. If you feel that it is negative or that you are getting taken advantage of in ANY way, learn to do what is best for you and kick that relationship to the curb regardless of the contract you may have signed because it takes TWO sides to form a healthy and collaborative relationship. Never forget that there is nothing mystical about martial arts instructors, as many good ones as there are, just as many are shit. Just like in life outside of the dojo walls, if someone shows you that what they tell you and how they act toward, or around you are different you need to seek out relationships elsewhere. You deserve better, demand it. Moving on. In addition to those relationships, and that tenacity, I learned to look for perfection in the execution of my technique, and by extension also of my body. In doing so I learned my physical limits, where I can push my efforts to greater gain and where I cannot, and on that reflective journey I learned what hardships and difficulties I can endure, and what I cannot. Tenacity, relationships, physical mastery, emotional and mental control of oneself. Worthless? Far from it.
Combat Sports (CS), as the title of this article would indicate is next. What is it? Competition. Healthy, safe competition. As a species we seem to attach ourselves to teams and athletes and colors and emblems and totems aplenty and I firmly believe that our love for combat sports is closely linked to an inherent sense of tribalism. How is it different than the other two (TMA and Self Defense)? I suppose the biggest difference in my mind is that it is geared solely to compete against an opponent in as safe of an environment as possible while still maintaining a semblance of "sport", or competition. Competitors know full well the risk, the rules and the expectation of performance from their teams, their competition, the governing bodies and themselves. That type of familiarity with impending "violence" is fairly limited to these competitive arenas, which is not so dissimilar from what is found in many TMA training situations, but a world apart from a scenario where an altercation takes place and only one person knows where it is going to occur, and the payout isn't one where both leave with trophies, paycheques or "exposure". Instead the payout tends to be more one way, and slanted so the victim doesn't know that the fight is happening until its well underway.
I would never go as far to say that CS doesn't have its own list of merits. Unlike with TMA, in CS our yardstick of success is much more tangible and though an individual will see their own growth and progress that is simply not the way success is measured in this arena. Strictly speaking in CS we pit ourselves against someone as much like ourselves as possible for the purpose of fair competition to see who will prevail in the fairest of competition. In this respect it becomes as much a battle of wills as a test of training and conditioning.
Think for a moment about how as a species, we constantly try to be more civilized to cut out the chaos of existence in the world we live in. It is one of the strongest driving forces behind the expansion of civilization. Now take a pair of individuals and say to them "You need to cut weight and train every day, running, coordination training, striking and sparring. There will be pain, lots of it. The food will be plentiful, but often you wont even have the energy after you train to eat it. Then when you have to cut weight to get to your allotted range to compete you will have to double your efforts and cut your fuel intake. 72 hours before you will have to also drastically cut your water consumption, 48 hours prior you will have to cut it completely. Then you will have to hop in a sauna... just to be sure. 24 hours prior you can eat and drink again. After you are done that you get in front of a crowd of your friends, family and strangers to strike and be struck, to rip and tear your way to the top of the scrum. Don't worry about losing champ, it won't happen with the effort you put in (we don't know about the other guy), it's impossible, the numbers don't lie (50:50).
In addition to mastering the adrenaline dump on a level that most of those who do not partake could never imagine, CS athletes become masters of fighting not only their opponents but the dichotomy of their own minds. as members of a progressive and civilized society as well as combatants in an arena of basic human instincts. At the higher echelons of sport these athletes possess a control of self that is different than what a person can find most anywhere else. Is it going to provide you with the same set of skills as TMA and Self Defense, no. But they wont provide you with this either.