Self-explanatory. Series who's primary focus is fighting would fit into this segment. Yu Yu Hakusho and Ranma 1/2 are classified as fighting series. But if you can, then please select a more specific keyword instead, such as "Gun-Action" or "Swordplay"; maybe some day we'll completely split up this category into some more terms of this sort.
A story which uses incorporates a competitive event as a primary component of the story line, but which is not of a martial-arts or violent nature. While both being cooking based series, Yakitate!! Japan and Chuuka Ichiban are good examples of this genre.