I guess the difference between a hatchet and an axe is a 1 hand or 2 hand grip respectively. With a hatchet, You can hold the target in one hand and chop it off with the other. The hatchet is rarely going fast enough or wild enough to remove a kneecap though. An axe is held with both hands and the path of the axe and all potential paths of the axe, should be controlled such that a miss goes into the chopping block, ground, or in the worst case, between your legs. Like swinging a baseball bat and hitting a home run, it takes some experience to hit the target squarely with an axe all of the time.

Actually when I was canoe camping in Canada I carried a medium weight axe. A saw would have been better for collecting wood as the axe was mainly employed in chopping down dead trees. It took less energy tp break the wood than to chop it.

Anyway I refer to ANY one handed, short handled light weight chopper as a hatchet, not as a short axe. A short axe is like my slash axe used for removing branches from felled trees. It weighs 3.2 pounds and has a 26 inch 2 handed hickory handle. My felling axe weighs 5 pounds and has a 3 foot hickory handle. If you really care - get a classic shaped hickory handle. Why hickory? Because it gives just enough to save your hands, is warm when is cold out and the shape guides your hands and arms as you use it.

I have hatchets too - but lets not confuse them with axes.
Jim <img src="/forums/images/graemlins/cool.gif" alt="" />
These are my own opinions based on wisdom earned through many wrong decisions. Your mileage may vary.