What makes one Martial Art different from another? Aren't all those Arts have the same end-goal: to protect oneself? How to choose right Martial or Fighting Art for yourself from the multitude of Styles and Schools?
Those are very legitimate questions asked by beginning students of Martial Arts.
The most common (and very good) recommendation by seasoned experts is "It doesn't matter what Art or style you'll choose, as quality and personal character of the Teacher are what matter. Look for the best Teacher, you can find, no matter his style."
When I can sign under this recommendation myself, it doesn't answer the original question. Choosing the right teacher over style is a (only acceptable) compromise, that beginners should make, but what is the other side of this trade-off? What I'm loosing by taking classes from great Takewando teacher vs. if it was Goju Ryu karate, Wing Chun style of old Chinese kung fu, Israeli Krav Maga, or Russian Systema?
When it's true that all Martial and Fighting Arts have the same goal to help you to defend yourself in face of physical hostility, they aren't exactly the same (this why there many of them, after all) and they achieve it by slightly different means.
So, what makes one Martial or Fighting Art different from another?
Any Art or Art style can be generally defined by three elements:
The strategy of Aikido is very distinct from Takwando and karate and strategy of Krav Maga is different from Wing Chun.
Aikido strategy based on contour-attack with it's no-first-move principal when Takewando and hard styles of karate work best in aggressive scenarios. Wing Chun is defend-your-ground style when Krav Maga promoting reflective defense and brutal reprisal.
So, when anyone of those Arts (with proper training) will help you to defend yourself, in self-defense situations it can pose variety of legal or social implications if defender, for example, will get into legal trouble by follow his style overly aggressive strategies. On the other hand, in some scenarios, demonstrated flashy aggressiveness can indeed defuse situation by discouraging hostility.
Strategy of a Martial or Fighting Art should be adopted to the rules and social norms of the place where it practiced. And in some cases it's easier then in other and the strategy of the style is a valid consideration in your selection.
Different Martial and Fighting Art put emphasis on different physical and mental skills and this, in large part, defines their tactic.
Aikido tactic based on good balance and precise circular movement, when Takewando and hard styles of karate relying on good physical conditioning.
Even within the (formally) same Art differences in tactic can be very significant: Goju Ryu karate vs. Shotokan.
The tactic is more evident in a style predominant technical set. Physical conditioning needed to perform those techniques are part of the training. So, see if you're comfortable with doing/training this.
Methods of training vary greatly between various Martial and Fighting Arts.
Some a sport based (Judo, Takewando, boxing) and some are based on kata training (non-sport karate and various styles of kung fu). Some combine fighting training with general physical conditioning (most Krav Maga classes)
Learning Martial Art is not easy task - look for an Art and a school with training that you'll enjoy.
Yes, in spite of all those differences, looking for the best Teacher is the only right approach for beginner student of Martial or Fighting Arts as every Art has flexibility to be personalized for needs and physical skills of any student. And this is what good Teacher will do.