Battle Axes were specialized versions of utility axes and were specifically designed for combat.
Many were suitable for use in one hand, while others were larger and were deployed two-handed.
Battle axes generally weigh far less than modern splitting axes, especially splitting mauls, because they were specifically designed to cut limbs rather than wood. Due to this, slightly narrow slicing blades are the norm. This facilitates deep, grievous wounds. Moreover, a light weapon is much quicker to bring to bear in combat and manipulate for repeated strikes against an adversary.
Hatchets were smaller variants of the regular one-handed battle axe. Although it lacks range and deals less damage when compared to its regular counterpart, its light weight makes it ideal for skirmishers and can also be used as a throwing weapon with the proper skill.