>>695476So much misinformation.
General distinction:
Hatchet - ONE hand use
Axe - ONE or TWO handed use
Small axe, therefore denotes:
Small = size/weight of head
Axe = shaft long enough to use with one or two hands
Personally I like something like OPs pic as it weighs marginally more than a hatchet but you can use two handed to generate more power.
Also, longer shaft = safer axe.