You're wrong.
There is no such thing as magic.
Magic:
"a power that allows people (such as witches and wizards) to do impossible things by saying special words or performing special actions."
It is impossible to do impossible things.
"an extraordinary power or influence seemingly from a supernatural source"
There is no such thing as supernatural. If it exists, it exists quite naturally. Nothing that exists, exists supernaturally.
Magic - Definition and More from the Free Merriam-Webster Dictionary
Miracle:
"an extraordinary event manifesting divine intervention in human affairs"
Extraordinary is not impossible. God exists. He does so quite naturally. God does intervene in human affairs.
"an unusual or wonderful event that is believed to be caused by the power of God"
Miracle - Definition and More from the Free Merriam-Webster Dictionary
Miracles are caused by the power of God.
magic doesn't exist.
But then again. Satan has powers as well. Perhaps he can empower individuals to perform seemingly impossible extraordinary actions as well. But since the source of that power is not God, it is not a miracle. We could I suppose call that magic.
Oh darn, it looks like I just contradicted myself. Oh well, such is life.