They're both DE-9 connectors, but the C64 joystick port is not serial. Each direction on the stick and the fire button are connected to one of the pins on the connector, and a when direction (or the fire button) is pressed that pin has a voltage applied. So effectively it's a parallel connection.

In a serial connection one of the pins is "send" pin and another is "receive". The device then sends data as a bitstream over those two pins.