What is the difference between a pickup for an active electronics guitar and a passive guitar?

Alembic pickups are low impedance.  Passive pickups are high impedance.
 
Bill, tgo

Is that true with all active pickups?
Are the magnets different?

I'm not an expert, but here's my take.  I think the general answer is that pickups aren't necessarily 'active', the electronics in the guitar are either passive or active, and pickups are designed to work with either an active or passive circuitry.  Bill is right in that Alembic pickups, being low impedance, need an on-board preamp, i.e. active electronics, whereas high impedance pickups don't.  In either case the pickups themselves aren't 'active'; the term 'active' refers to the presence of a preamp in the instrument and a power source for the preamp circuitry.  I think there may be some pickups that have a preamp built in to the shell rather than separately installed in the instrument.  There's a good wiki on the subject here.  Some manufacturers call their pickups active pickups, but again, technically, I think this refers to the fact that they are designed to be used with a powered on-board preamp, i.e. active electronics.  That's my understanding, but I'm not an expert.

Thanks Dave. I have also heard the Ceramic magnet vs Alnco magnet argument.. I dunno..

heres a company that uses neodynium magnets, they also use a high z for the bridge a medium z for the neck, i really want to try them out, my dad was talking to a representative of theres and he said that they were starting to experiment with 1 meg pots instead of the traditional 250 or 500 k
 
http://www.q-tuner.com/
 
~Taylor
 
(Message edited by tmoney61092 on July 31, 2010)

As far as I know, it seems that you affect Impedance with how many turns you make on the coil... Less turns means lower Impedance and a broader frequency response. But, as this means less signal, you must use a buffer to rise it up (the main function of an onboard Active Preamp).