The obvious difference you would notice is that the Flight Director system moves the command bars on your display. If you have it in "Alt hold" and "Heading" modes, then turn the heading bug, the command bars will move - you follow them, and find you're turning onto the selected heading. Select a 1500 fpm descent on the FD, and the bars will pitch down. Follow them, and, lo and behold, you're dropping at 1500 fpm.
The autopilot switches in the servos on the relevant control surfaces, and it follows the FD commands instead of you.
That's a very simple approximation - hope it answers your question.