Originally Posted by
unworthy1
the lower example is called (by most) a "Maul" and has differences to most other mallets in the shape of the striking surface (curved wood in this case but can be plastic or hide) plus how you use it:
"Rocking vs. Hitting- Mauls are used with a rocking motion of the wrist, as opposed to the hammer-like hitting motion of a mallet. While it takes some getting used to, using a maul over a long work session takes less energy and puts less stress on the body."
YMMV
Some more explanation, hammers generally have a hard, metal head and are used for driving nails, breaking things, or shaping metal. Mallets, on the other hand, typically have a softer head made of materials like rubber, wood, or plastic, and are used for striking surfaces without causing damage or for driving tools like chisels.