A polearm is a weapon which, in general and in its basic formula, takes the form of a long stick, or pole, with a bladed weapon fastened onto the top. From this it is developed based on the nature of the weapon fastened on. An axe on a long pole becomes (perhaps unsurprisingly) a pole-axe: it has a small chopping head, but a substantially longer reach than arms'-length.
Pole-hammers never gained the same favour -- by its nature, the hammer needs to be swung and to impact square(-ish) on. Swinging it on a pole takes too long and is too easily avoided.
Language being the wierd thing that it is, the original word had nothing to do with poles. "Poll" is Middle English for "head" so first there was a "pollax". Over time, this was corrupted into "poleax" and from that came the "polearm".