The marital aspect of the martial arts pertains to fighting and violence, while the art aspect pertains to peace and calm. The two aspects combine to form the way, a separate aspect that unites the martial and the art so the violence may be controlled. Boxing is a method of fighting but there is no art, and no way, so there is no control over the violence. Boxers live for the violence, it becomes a major part of their lives, and many lack control of it. The same holds true for wrestling and modern mixed martial arts. In the classical, traditional martial arts, the way develops morality and a sense of inner being that allows practitioners to control their own violence and the violence of others around them. Without the way, there is no control over the violence.
The differences between combat skills and martial art skills may be compared to the differences between listening to a band in concert and listening to the band from a recording using headphone. When listening to the band using the headphones while sitting in your recliner, all extraneous sounds are blocked and you hear the nuisances of the music. You hear picks scrapping the strings of a guitar and you hear the fingernails of the pianist tapping on the keys. You may appreciate the music and appreciate how well the musicians perform. You hear the music of the band in its purest form, but only after it has been modified by numerous sound technicians. After listening to the music, you feel satisfied and, if you want to feel satisfied again, you just put on the headphones and play the music again.
When listening to the band in concert, you are immersed in the music. You not only hear the sound, you feel the sound over your entire body. You are jostled by the crowd; you hear them and feel their emotions. You in the mist of the action, experiencing the music of the band in its rawest form, you hear all the mistakes and off-key notes but you "feel" the music. After a concert, you feel alive and fulfilled, but the only way to achieve the feeling again is to attend another concert.