Well, you can set up a parent constraint with more than one parent. Example: you could parent contraint the mace to a character's hand so that it stays there but you can also parent constraint it to another character's hand at the same time. You turn the constraint on for the character who is holding the mace and turn it off for the guy who isn't holding it. Now, you can have the first character hand the mace to the other character or set it on the table then have the other character pick it up. You do this by simply switching the constaint on and off for each of the characters. The reason this works without having the mace snap when switching constraints is because the parent constraint maintains the childs position just like when you use parenting.

If you have a sphere located at 0,0,0 (x,y,z)and another sphere located at 2,0,0 and you use the orient constraint and the point constraint with the 2 spheres instead of parenting them, the constrained sphere (the child) will keep its own pivot point centered within itself. So, if you rotate the "parent", the "child" will also rotate but it will rotate from its own pivot point rather than from the center point of the parent. Also, if you move the child around by translating or rotating it, then move the parent, the child will snap back to its position before you moved it.

If parenting the two spheres together, the child will move as you move the parent but it will also keep it's original relationship to the parent. In other words, the parent will guide the child around (like a parent holding a childs hand). It's ok for you to move the child around without the parent because when you move the parent, the child will always follow from its current position. It will not snap back like it will when using a point/orient constraint.

Well, the Parent constraint is just like parenting except that you can hook up more than one of them and you can turn them on and off.

It will make more sense if you sit down and play with Parenting, parenting constraint, and also point and orient constraints.