Kung fu, Karate, Kali, Kendo, and a whole host of other martial arts. One hard thing to do when you’re writing is to convey the idea that a character has practiced a specific fighting system, or to create an adequate distinction between two characters using different ones. Most of the time, it doesn’t matter, but sometimes it is more important. Any time that you mention them having practiced something specific, then ideally that should come out in any fight that shows up with them.
So how do you do it? One thing is to get a reasonable knowledge of whatever martial art you’re portraying, or at least of the core flavour. Bruce Lee made the point that there aren’t really any different ways of fighting, because we have two arms and two legs, the ability to throw the same moves. Yet there is often a difference in feel, and it is that quality of movement than is often the easiest thing to write.
You’d also want to stick to the core of the art. In theory, most martial arts contain most things to some degree, but the things people think about are the things at the heart of them. When people think about Taekwondo, for example, they think of fancy high kicks, or they think of throws when describing Jujitsu. Yet Taekwondo has throws and Jujitsu kicks. The point is that when conveying flavour, you can’t focus on that.
If you were writing, for example, a swordfight between a kali practitioner and a kendo one, then of course the kendoka would use a two handed grip rather than using two blades, and the kali fighter would have a sword and dagger. The kendo fighter would probably move in fast, controlled, focussed movements with a lot of precise power. The kali fighter would probably move in at close range with lots of rapid striking, triangular footwork and trapping. It’s not about portraying the whole of an art, but just one more way to give a distinct feel to a character.