There is currently several types of axes.
There are two types of stone axes: the simple stone axe and the stone axe. The first does not have a handle, the second does. Stone axes perform faster than simple stone axes. However, stone axes are slightly harder to make.
Bronze axes work the same speed as stone axes, but when you use it you get 2 small/tiny wood instead of one. This makes them much more efficent. Also, you cannot have a bronze axe without a handle.
Axes can chop medium and small wood.
Medium Wood ------> Small Wood
Small Wood -------> Tiny Wood
Axes are rather simple to make.