A person with "fighting spirit" is a person with the following characteristics: strong-willed, motivated, doesn't give in, sticks it out, struggles through, gives all, has a lot of self-confidence, tries always her/his best, overexerts her/himself. That would mean mental strength (fighting spirit) is a combination of motivation and concentration.
A mentally strong player will be high motivated and high concentrated throughout a tournament. And he/she stays in this optimal state even when problems might turn up. She/he stays mentally strong because even after a loss, he /she can motivate her/himself again, because knowing how after losing concentration to win back optimal concentration.
Mental strength develops out of the deep belief to be able to manage it even when it looks bad in a match. James E.Loehr defines it like this: "Mental strength is the skill to play at your limit even in competition". Competition is some kind of a test, which means additional pressure for a sport; you need mental strength to be able to "neutralize" the circumstances and to reach your optimal capabilities.
It seems to be that being in a competition diminishes the capabilities of a sport. It depends on our believe in our skills whether we really can repeat practice achievements in competition or not. The self believe arises from the conviction you really practiced hard and out of the knowledge of your own strengths. And a sport has to be aware that even after a total failure live will go on, that wins and defeats have a place in sport. Only a person who had endured defeat and put it away really deserves wins. "Failure is always part of success" (Erik Weihenmayer, who climbed the seven highest mountains of the world though being blind)