Air battles is the best name for all the battles that took place in the Air. An other possible term is: Aerial battles.
Sea battles is the best name for all the battles that took place at Sea. Other possible terms are: Naval battles, Nautical battles, Naval engagements, Nautical engagements, Naval action,and Nautical actions.
It has been decided that, in the name of common sense, these two terms would be the best available compromises.
This logic can also be followed in the (future) subCategory: River battles, instead of Fluvial battles. The second term is virtually unknown and almost never used.
It is the same logic with the (future?) Space battles, instead of Sidirieal battles or spaceial battles.