Maces were probably an evolution of the hammer as a weapon.
While a hammer is common enough, as a weapon it is not that effective. It does not have enough weight to go against armor, nor does it have enough reach. Maces don't have reach either, but they have much more kinetic energy due to their weight.
More the other way around. The war hammer evolved to defeat plate mail. It was a late medieval development.
The war hammer is much different than the smith's tool. It is lighter, has a blunt end on one side and a pointy pick on the other. It is the pointed pick that is interesting, as it allows the full focus of the blow to be concentrated in a small spot. The blunt side is pretty much the same as a mace.
Skyrim doesn't really do weapon effectiveness vs. armor type so it doesn't really matter that much from a general game play PoV. It becomes more of a variety/role play thing ... which is why mods are a good thing

.
Also, don't confuse a Skyrim mace with a real mace. A real mace had a head about the size of a fist, not a bowling ball. Real weapons were light and fast. Fantasy stuff is double to triple to 10x the size of a real weapon. You don't need to swing a 10 lb thing to split somebody's head open. 1.5 lbs of steel is quite enough. Anything more is dead weight for little value.