In answer to your question, there is no difference in the wires because a lighter element isn't polarized, in other words, hook either wire to positive, and the other to ground. That's why both wires are black.
A cigarette lighter has only one power wire, and a ground which usually consists of the socket assembly that screws into the hole in the dash. The ground is achieved by the housing grounding to the metal dash. The ground could also be a separate wire these days since a lot of what used to be made of steel is now made of plastic.
The wire that leads to the center terminal is the power wire. The wire that is attached to the case or side of the unit is the ground side.
the power wire is usually a colored wire like red,blue. the other wire should be white,green or a bare copper wire.
