If we are to look at the science world, we will see that power is the ability to do work. The ability to make things been done while we can say authority is the right to get something been done. Who would you rather be, will you be the fellow who has the power or the one who has the authority. Let me know your answer in the comment box.
You are not only meant to be healthy, you are also meant to have so so much authority over certain things which might be disturbing you. Things like sickness, diseases, affliction, inflections that even when those things touch you, they instantly vanish away.
There might be instances where you have the power of divine health but you might be lacking the authority to make someone else health. You might have power but you may not have authority. But it is always possible to have the both if you wish to by God grace.