There is no such stuff as “Static” electricity or “Current” electricity. These are very mixed-up concepts. They’re not correct ideas.
Normally we do divide the science of electricity into Electrostatics and Electrodynamics.Think about it: should we say that there are two types of matter, Static Matter and Current Matter? No, that’s stupid. Statics and Dynamics are just subject areas. And the field of Hydraulics is divided into Hydrostatics and Hydrodynamics. Are the two kinds of water called current water and static water? Nope, silly. But it’s just as silly if we believe in “static” electricity and “current” electricity. The fields of science are divided into two types, but not the matter, or the water, or the electricity.
So, “static” electricity is not electricity which is static. Instead, it’s electricity which is imbalanced. If we have the separation of opposite charges, with more positives than negatives over here, and more negatives than positives over there, then we have a charge-imbalance. The imbalance itself is the so-called “Static” electricity. It’s also called “charge separation” or “net-charge.” It really has nothing to do with being static. The science of Electrostatics deals with charge-imbalances and the forces of electric attraction-repulsion.
There is no constant and continuous stream of static electricity, because then it would not be static.
So static and current (continuous flow) of electric charges are two views of the same charges.