Also, just like a choctaw throwing stick:

I've always liked the look of the Stielhandgranate more.
This is another interesting video about it,
http://www.youtube.com/watch?v=HB9o-Tmxyv8

The potato masher had a thinner skin, and a heavier explosive weight.  It was designed for a storm-trooper tactic:  small groups advance under cover of artillery fire, not shooting their guns, but using grenades to take out enemy bunkers, hoping the grenades are mistaken for the artillery- and the enemy keeps their heads' down, allowing the storm troopers to advance to a command/communications point, and destroy it.  A "frag sleeve" was developed later.
The pineapple was designed to throw metal- but the explosive charge was too small. (only 55grams in the Mk2 Pineapple).  This produced large fragments that were lethal at long ranges, but the probability of a hit was low (bigger fragments= fewer of them).
The best modern grenade designs use pre-formed fragments, usually ball bearings held in epoxy.  This gives a nasty storm of metal at close range, but the small (1-3mm diameter) ball bearings lose velocity quickly.

it was also considered an "offensive" grenade meaning that it relied primarily on the explosive itself to cause damage rather than a fragmentation effect.