The first kind are living punching bags that seem to consist of two (possibly three) human souls grafted to tall pillars and chained there to suffer for all eternity. They can be freed with a few shots or a swing of the player's sword.
Trapped Souls can deal damage to characters or minions who happen to stand in their range, but they are largely harmless. They cannot drop items, and are usually noticed only when all summoned creatures and mercenaries run off to kill them when you would prefer your minions stay put and fight against the monsters that pose a real threat. The Zookeeper build has an especially tough time controlling his minions in Hell difficulty in the presence of Trapped Souls.
The second type of Trapped Soul is a container. These souls are chained down on the ground where they can do no more than wobble in their torment. Striking them may free them from their agony and reward you with treasure.
While unlike the former versions, these Trapped Souls do not have a life bar, they may still require more than one kick before they are freed.
Trapped Souls are not rigged with any of the usual traps, but some may expel jets of fire before collapsing. Standing too close will result in damage.
As these Trapped Souls are containers, minions will not actively hunt them down.