The Hammer is one of the easiest tools to make, after the digging stick, and would have been one of the first weapons (probably also after stick). The variations come largly out of work. The blacksmith had a larger hammer than the carpenter. Where the carpenter would use one hammer he would need a small one that had a surface and possibly a point, the blacksmith would use paired short hammers since he was used to holding a heavy hammer in one hand and the steel object in the other. I don't know the history of the mellon hammers but the octogon hammers were used to hit nails into corners. There are also many variations in each country. Masonry hammers, ripping hammers, sledge hammers, peen hammers and more are available from any hardware store. If you look at the catalogs for other countries you will see an even greater variation in hammers. As a tool, hammers are incredibly specialized and are usually the first tools to take advantage of new technology. Hardened steel heads, shock resistant handles, unbreakable handles, and dead shot hammers are all examples of tools that would make a barbarian cry out in joy.
The carry over into war would have been (and still is) easy as there is no difference between hammering a nail, wood, steel, or your opponents head. The Precision involved would have been less than for, say, the axe. The power and stability would have been greater due to the weight. With the new technologies available, the hammer can replace most other weapons in function and capacity. They are cheep, light and strong enough to replace the stick as a beginner weapon and tends to resemble the more advanced, combination, or master level weapons when you look at some of the more complex hammer designs. It will be one of the heavier weapons in Any 18 classes of weapons grouping, allowing for any specialty weapon of course.
As far as style goes: If your style uses both hands equally (karate, hung styles) then the double hammers will be the tendency. If your style uses big hits (choi li fut?) then a single one handed hammer will be usually chosen. And if your style likes footwork, evasion over blocking, and power then the long Hammer will be favored.
The benifits to stance and technique are pretty much the same across the board with each traditional hammer variation being taught to strengthen specific skills. Most styles will have all three variations with one of them being considered the advanced weapon and the other two being levels more basic.
I tend to think of the hammer as an Ape weapon but tiger uses it to build short power and dragon can easily use it as a weapon although they don't focus on its training much.