Condition I. Copper sulfide, which has a grey to black color, is most likely the result of the reaction to moisture (humidity). An oxygenated copper is more reactive with water being reduced to to a sulfide at the surface. The sulfide is a penetrating film which will also cause higher resistance in the connection and a resultant lower voltage. It is difficult to remove. The typical connections seen in this forum are set screw mechanical compression, which will loosen up over time due to the creep of the soft copper under a compressive force. Higher resistance and heat will result under load. The heat along with some air moisture can produce this condition.

Blackening of the copper stranding can also be accomplished by overheating and reducing with a torch when attaching lugs.
I have also found the blackened condition under the insulation on improperly cleaned copper stranding which was covered up during jacket extrusion processing.

Condition II. Copper sulfate. When overcharging a lead acid battery gassing will result. If the gasses contact bare copper cable (wire), a corrosive product, copper sulfate, will be seen on the bare wire.
This corrosion product will typically be blue / green in color. It can be removed fairly easily but the base copper material will have been consumed in the process leaving you with a severely damaged wire or connector in need of replacement to maintain the integrity of the circuit.