I can't quite recall at the moment the source, but I do remember the criteria more or less, of what defines the difference between a poleaxe and a halberd.
I think it was something like:
- A shaft at least 10 feet in length.
- A spike at least 1 cubit in length.
- A spike or hook at the back.
- An axe blade that is either straight or concave and is angled downwards toward the user.
I think it also said something about it being a formation weapon being used by heavy troops in tight formation, being used more so as a pike rather than an axe.
Which kinda makes sense, if you take a good long look at one. If you swung it like an axe, you'd hit the guys either behind you or beside you, which would probably make them not like you very much.
I figure, how they fought with them is you'd try to pull the other guys out of their formation and pin their halberd with your own so your buddies can stab at their less armoured bits.