Static electricity happens when we pile electrons on the surface of an object and they can't get away. It can also happen if we rub electrons OFF an object. When electrons move, we call that current.
When we rub two rocks together, if they are the right kind of rocks (quartz) and it is dark enough, we see sparks. These sparks are caused by a different effect, although it also has to do with electrons. The rock is made of crystals, and the atoms in the crystals are connected with very strong forces. When we crush or break the crystals by banging or rubbing the rocks together, we release some of that energy. The energy excites electrons in the atoms, they bounce around and as they relax back into place, they send out light. We see this light as sparks. This is called piezoelectricity.
By the way, you can see the same thing in a very dark, like pitch black, room with Wint-O-Green Lifesavers as the sugar or flavor crystals break. (It's not polite to chew with your mouth open unless you are in the dark with Wint-0-Green Lifesavers. Then it is science!)
