Hammer
Hammers have all one thing in common: weapons attached to a burst motor with a long extender between the motor and weapons.
Hammer (vertical)
Real life examples: Frenzy, Killerhurtz, The Judge, Diesector (partly)
RA2 examples: Grog, BEAR, Bushido
A bot that basically brings down a weapon on the opponent. Can be everything: a bear claw, an axe, a katana...
A hammer is basically better against bots with a vulnerable roof (rammers). It can be efficient against a bot with a lot of extenders and against horizontal spinners if built well.
Side Hammer
Real life examples: Splinter (Robot Wars)
RA2 examples: Atom Smasher
Basically, kind of an hybrid between a clamp, a thwacker and a hammer. Rather than bringing down the weapon, it is bringing it from the sides, like a claw closing on the opponent.
This type hasn't generally the damage values of a normal hammer and does worse against horizontal spinners, but can be made invertable then.
If you want your hammer to be damaging, then put several weapons on your hammer head. A hammer head featuring three razor tips is way better than a simple sledgehammer.
Trivia
Hammers are a rarely built type. Often, a newbie builds one, but then often switchs to another bot type.
A few builders still perpetuate the species, mainly Sage and in a lesser extent Naryar.