What is the explicit difference between the ground and neutral wire in 110V systems?
Grounding
The bare copper (grounding) conductor is a safety system that provides an effective ground-fault current path, and should only ever have current it in the event of a fault. It provides a low resistance path back to the source, so that a fault can be cleared by the breaker (trip).
Grounded (neutral)
The grounded (neutral) conductor is a current carrying conductor, and is used to complete the circuit back to the source.  In normal use, it will carry the same amount of current as the ungrounded (hot) conductor.
Touching this wire is not recommended, as there is actually current flowing through it.  However, as it likely provides a lower resistance path back to the source, most of the current will flow through the wire instead of you. If there's enough current flowing, or you provide a good enough path to the source, touching this wire can result in large amounts of current flowing through you.