I suppose, put in the simplest terms, the FD shows you what to do (according to the FMC or MCP) and you then move the controls to follow the directions. If the autopilot's engaged it will move the controls for you.
As for where and when we use what. The FD is displayed all of the time and the autopilot is only engaged once we've had enough of hand flying or we're required to for an Autoland.