Azurite = Cu3(CO3)2(OH)2
Malachite = Cu2(CO3)(OH)2
As you see, they're very similar chemical formulae. The are both made up of copper, carbon, oxygen and water in slightly different configurations. My background is actually in geology; both are typically found near the surface as copper ores react with water and oxygen; the latter being of course found in much greater amounts near to the surface as it's carried down dissolved in water. The copper in coins will react in exactly the same way. Both minerals occur in very similar conditions, and are often found together, though malachite is commoner.