Yes, that is your ground wire.
That second "black" wire actually isn't a black-insulated wire at all; it's bare copper that's badly tarnished. You can see that it's a slightly different color than the other black wire, and also a little thinner (because it is not insulated). If you scrape it a little bit, you should see shiny copper. Bare copper always indicates a ground.
I would recommend taking a bit of sand paper and cleaning the oxidation off before you attach it to anything else -- it'll make a much better electrical connection that way.