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 weapion 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.
Other things tied on to poles were knives or daggers, to make an impromptu spear, for thrusting, or a cleaver, which made for a stouter than average cutting weapon, again with the extra reach.
Once these weapons became established as useful, armourers and smiths began making them to custom, with the weapon end firmly and intentionally fastened on to the pole.
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.