From what I gather, they are slightly similar for they have the key word "supernatural" but not the same. Magic is performed to give appearance of the supernatural and miracle occurs in the physical and attributed to the supernatural. Someone has to perform it for it to happen that is magic,for instance,'a magic show' is organized by a magician who is someone that makes something seen to be impossible possible. Something that comes naturally is a miracle meaning nobody makes it happen. A miracle just occurs when one least expects it while magic is expected.
In essence, magic is fake and a miracle is real. It doesn't mean one cannot have both in life.