Write out your signature. Write it out with the opposite hand. Both signatures were being driven by a brain that knows exactly what it looks like, yet, the result was different. Why?
First, the skill is different. One hand is more practiced than the other, but what that means on a deeper level is the brain would have to send different electrical impulses to move each hand in the same motion, but it is only practiced with one of those impulse sets.
Secondly, the pen or pencil you selected is comfortable for your typical writing hand, not necessarily your opposite one. It may be too heavy, or fit differently between the fingers, or be optimized for a certain hand in some way.
The result then obviously lies in the mind, the skill, and the tool. For this example, the tool has the lowest impact, and the mind and the skill are inextricably linked. Most often however, people focus on the tools. Tools are the easiest to swap out. They don’t require much commitment, nor development, but the true power lies in the mind and its ability to develop skill. That is an area that is often neglected.
Focus on your mind and skills, it will pay dividends.