Definition of a battle:
a. An encounter between opposing forces
b. Armed fighting; combat
c. A match between two combatants
Thus applying battle for 2 or more people fighting each other is also correct, given that they are armed or hand-fighting in a serious match. Also within Danbooru, being armed is more than just gun and sword. The characters can use martial arts, magics, fantasy items, and sci-fi equipment.
For trivial conflicts or arguments, use fighting.