Magic is considered to be methods by which mankind may use various rites, rituals, incantations, etc., to cause the laws of nature to "bend to their will". The English word itself is derived from the same root as the "Four Magi"; Persian 'shamans' mentioned in the New Testament. Examples of magic are "Voodoo rituals to cause an indifferent individual to fall in love, making a Voodoo doll with a piece of someone's clothing or hair and sticking pins into it while chanting particular words in order to cause harm, etc. .
Miracles are something entirely different. Judaism considers a miracle to be a Divine Intervention which completely overrides the laws of the natural world to effect the Divine Will. Prayers and appeals to The Creator, in and of themselves, do not cause a miracle to occur. When a true miracle takes place, a "supernatural" (outside of all known laws of nature) event takes place, and this event can not be explained using "reason" or the scientific method.
In colloquial use these terms are "thrown around" with abandon. People refer to "magic" to describe the tricks and "illusions" of professional entertainers. Closer to the actual definitions are the rites of Wicca, Voodoo, Satanic Cults, etc...all of which lay claim to affecting change through human intervention.
We also misuse the term "miracle" to refer to any circumstance deemed favorable to us, such as "It's a miracle that we weren't hit by that car". "I got the job!"..."It's a miracle!" Perhaps lubab can enlighten us further on the various degrees of Divine Intervention, but most things we call a miracle today fall short of The Parting of the Red Sea, or The Sun Standing Still to allow extra hours of battle, etc.