A Wizard’s Wand is far more than a sort of carved stick. Besides the appearance itself, and the ability to actually touch it, there is very little that is normal about this magical construction.
A Wand is practically nothing. It has been stripped of nearly every aspect of existence so that it can serve as a magical container for storing various elemental qualities. This simplicity of existence is also what makes them so useful as a casting aid—inside the Wand there is nothing to disrupt the magic as the Wizard shapes it into a spell. They also have the added benefit of naturally pouring the full energy of stored qualities into any spell that uses them, thereby boosting the effect without extra effort on the Wizard’s behalf.
This is in stark contrast to a Wizard, who contains all sorts of interesting elemental qualities required for life, and whose bodies tend to produce Spell Bursts as a result. The human body is also ill-equipped to store extracted elemental qualities, and doing so has very unpleasant side effects.