Martial Art vs Fighting Style

A "Martial Art" could literally be anything you practice to get good at in order to defend yourself or hurt others, ranging from Parkour to driving in a destruction derby, to archery. Even more confusingly it can refer to the differences between cultures in practicing various techniques (as with "karate" versus "kung fu",) or it could refer to very specific techniques such as "the art of throwing a good straight punch" or "using situational awareness." But most of the time "Martial Art" refers to something more specific called a "fighting style."

Boxing is certainly a martial art, but I would say that it isn't a fighting style. Mayweather is a boxer who has a career of 50 undefeated fights. Tyson is a boxer with 44 knock outs. If martial arts were the same thing as fighting styles, these two fighters would be very good at most of the same strategies, but in reality they are both known to have very different yet common fighting styles known to exist within the martial art of Boxing. Even their fighting stances have well established names, Peek-a-Boo for Tyson's hard-hitting front stance fighting, and Philly Shell for Mayweather's careful and precise side stance fighting. Other fighters who trained with Tyson's trainer had basically the same style as Tyson, and Mayweather's Philly Shell is a multi-generational family fighting style:

I trained with Vern Miller before Margaret McGregor's male vs. female boxing match in 2000 (she won.) Vern Miller was more known for his kickboxing fighters, and also taught Tai Chi and Choy Li Fut. Choy Li Fut was his primary "martial art" and the combat sports and Tai Chi were part of that. The fighting style he drew from his martial art involved a front orthodox stance, left foot forward, unless you were left handed, then you fought south paw, right foot forward.

A about a decade ago I had a close friend train at Bumble Bee's Boxing in Seattle, the most famous boxing gym in the Seattle Area. We were surprised when it turned out they fought from more of a side stance, and that left handed people who trained there also fought orthodox. These were two very different styles of boxing in an hour's driving distance from each other, and what style you boxed at had everything to do with who the most experienced instructor was at they gym you trained at. Here's a side stance fighting Bumble Bee's fighter verses a more front stance Mexican-style boxer:

We can contrast boxing, which is a sport and a martial art but not a fighting style, with Judo which is both of those things AND a fighting style. Most Judo black belts can demonstrate all of the 67 throws of Judo. However when they spar, most Judo black belts will focus on only the throws that work best for them, typically around a dozen of the 67 throws. Which dozen throws depends on the individual black belt. Going by this we would be tempted to say that each Judo black belt has his own style of Judo, but the fact is almost all Judo black belts train in very similar techniques in very similar ways, and again they can all do all 67 techniques. So Judo is clearly a fighting style even though it is also a sport and a martial art.

The name of a martial art is not always specific enough to know the fighting style taught there. Something as broad as "Kung Fu" or "Karate" will never tell you the fighting style, as there is a world of difference between the fighting styles of Olympic Karate and Kyokushin Karate. In Kumite Point Fighting (like the tournaments you see in the Karate Kid/Cobra Kai franchise) because everyone seems to be fighting more or less the same way, it looks like they are all doing the same fighting style. However, the competitors train in extraordinarily different ways, and could come from all sorts of martial arts backgrounds, and for many of them the Kumite Point Fighting might not even reflect how they do sparring most of the time in their training. Because most Kumite Point Fighting participants come from different fighting styles, Kumite Point Fighting is NOT a fighting style. 

Mixed Martial Arts (MMA) is most definitely NOT a fighting style. Even for the rare fighter that only trains for MMA and never trains in other fighting styles, their specific gym they train at is guaranteed to have their own MMA fighting style that will be significantly different from many other gyms that also only train for the sport of MMA. This is not to say anything negative towards the Martial Arts of combat sports athletes. Mike Tyson's Peek-a-Boo fighting style would be devastating in a street fight, a very practical option for many self defense situations, a potent fighting style in and of itself by traditional martial arts standards. "Martial Arts" is a very broad term that also includes "fighting styles," and fighting styles are ways of training for using specific techniques and strategies in a fight.