Is electric current and current the same thing?

Not really. You can compare them with the analogy of water flowing through a pipe. For water to flow, there must be a pressure difference across the ends of the pipe. An electric current is a movement of electric charges along a conductor. For those charges to move, there must be a voltage (more accurately, a 'potential difference') across the ends of the conductor. So a potential difference is required to cause current to flow.