Electricity is movement of molecules?

You need to learn the meanings of the words. A molecule is some combination of atoms bonded together, but no net electrical charge. If a molecule gains or loses an electron then it has a net charge and is called an ion. If an ion moves, that is an electric current.

Electric current is a flow of charge, not necessarily movement of particles. If you look at a row of marbles and you hit the first marble, the hit is transmitted through the row, but the marbles don't move enough to notice. That is how electric current flows through a conductor. The electrons don't actually move much, only the charge is carried through.