To put it frankly, some have little sense.
For example "Sword of war" or "War sword"
In case of axe, it does make sense, because axes were used for both combat and cutting wood. So the name "war axe" or "battle axe" means that this particular weapon is designated for the use in combat.
On the other hand, swords had no civilian appliaction, they were dedicated weapon. Therefore, the adjective "war" or "battle" is redundant. And what does the name "arming sword" mean? I could not find out. Is it supposed to indicate that you can arm yourself with it?
By the way, please note that the commonly used name "broadsword" was created by accident by 18 century writers who wanted to distinguish the later used rapiers and foils with thin blade from the medieval cutting swords with broader blade. In medieval times though, no such name was used.
For example "Sword of war" or "War sword"
In case of axe, it does make sense, because axes were used for both combat and cutting wood. So the name "war axe" or "battle axe" means that this particular weapon is designated for the use in combat.
On the other hand, swords had no civilian appliaction, they were dedicated weapon. Therefore, the adjective "war" or "battle" is redundant. And what does the name "arming sword" mean? I could not find out. Is it supposed to indicate that you can arm yourself with it?
By the way, please note that the commonly used name "broadsword" was created by accident by 18 century writers who wanted to distinguish the later used rapiers and foils with thin blade from the medieval cutting swords with broader blade. In medieval times though, no such name was used.