They have the same type of blade... there is no way to distinguish them, except by the way they work.
The battleaxe would have two sides.
I google imaged "Hatchet" and nearly every picture was:
-Long handled
-Flat or very close to flat blade
-Wooden handle enters the metal blade, rather than other way around.
The major reasons for these differences is that with a hatchet, you're looking to chop a solid piece of wood in half. The difference in balance, which caused by the way the handle and blade join and the length of the handle, makes it ideal for chopping, and the shape of the blade wedges a purely solid object in two.
A tomahawk is a one handed combat weapon. The blade and handle are different so that they can also be thrown accurately.
tl;dr: You don't fight with, nor throw hatchets.
Of course, I could be wrong seeing how I'm judging this based on how I see it. If you wish to consult a wiki or something feel free.
