In regard to electron current moving through the wire and load, the anode is negative the cathode positive. In regard to the ion current, the anode is positive and the cathode negative, since the positive ion coat the anode and make it appear positive. It is standard to table the electrodes in regard to the electron current. In either case, the anode is the metal that give up electrons to the wire and positive ions to the solution, and the cathode accept electrons from the wire and positive ions from the solution.
The simple cell has a lead anode (+) and a lead dioxide cathode (-), immersed in sulfuric acid. As current flow through the wire from anode to cathode, it light the bulb. A cell in storage battery has several positive and negative plate, separated porous insulators.