Many theists believe in miracles but not in magic. Most atheists I've talked to dismiss both miracles and magic. It seems to be that there's a close relationship between the two. Magic is defined as "the power of apparently influencing the course of events by using mysterious or supernatural forces." A miracle is said to be "a surprising and welcome event that is not explicable by natural or scientific laws and is therefore considered to be the work of a divine agency."
To me, the difference is primarily in that, where magic is concerned, we recognize that the magician is performing a trick by sleight of hand or some such thing. We know that it's explainable, even if we can't figure out how he does it. When we describe something as a miracle, we simply say that there is no explanation for what happened. The theist will give credit to God and the atheist will say that there is a scientific reason behind it, even if we can't understand what it is.
In my opinion, magic is something certain humans can perform that appears to baffle other humans. Miracles are something God can perform that appears to baffle all humans. Other than that, there is really no difference. Neither one breaks any laws of nature, but both require us to recognize that there are events in life for which we have no explanations. This is not due to the fact that they cannot be explained. We just haven't found the answers to them yet.
Magic tricks require illusions and a gullible audience to work.
True Miracles require non-doubting prayers, faith and the mercy of God to work.
Fake Miracles require stuntmen and a lot of showmanship