I like the gist of Phoenix' reply. But I'll add my 2c worth (as usual!
)
An autopilot pitches, rolls and trims the aircraft to maintain the desired flight path.
A flight director commands YOU to pitch or roll the aircraft to maintain the desired flight path.
Both the AP and the FD get their 'instructions' from the Mode Control Panel. The MCP selections might be IAS in a climb or a descent, levelling off at a preset ALT, or VNAV input from the FMS (FD pitch bar) as well as holding a HDG, a VOR radial or flying an LNAV path (FD roll bar).
On receipt of their instructions, and AP will try to do what you have asked for on the MCP all by itself, and a FD will instruct you how to push/pull/turn to acheive the desired flightpath.
The FD will do this within limits (BAe146 example) being: FD roll bar will command up to 25deg AoB normally, reducing to 10deg AoB when established on a LLZ beam. FD pitch will command up to 20 NU. And I think a +1.5g/-0.5g limit too (back to the books, ITCZ!)
So when a FD bar moves, it is saying "pitch up to maintain that speed/altitude, thats it, ok pitch it down, now start rolling to the right to intercept the localiser, more, more, ok roll off the bank..... etc!
Raw data is FD off.
Another example.
Learning to fly IF, you probably heard your instructor breaking the task down into.. where am I, where do I want to be, what do I need to do to get there..
Raw data, your instrument panel is simply telling you how things are and where you are right at this very moment (or, really, a fraction of a second ago, once you account for lag in some instruments). = Where am I?
Adding a MCP then 'tells' the panel where you want to go. = Where do I want to be?
The FD then tells you to pitch and roll the aircraft to match your MCP selections. = What do I need to do to get there?
Not inviting argument or finer points on FD vs attitude and performance flying --- save those for later!