The Resuce course is something much different.  You have to complete Emergency First Responder training on first aid and CPR.  You then learn about and practice a variety of methods for dealing with divers experiencing difficulties, including panic, unresponsive divers under water, and unresponsive divers at the surface.  The final checkout dive involves responding a diver pretending to be unresponsive and face down in the water; you have to get them face up and do rescue breathing while you tow them to the beach and get them out of the water.  I found it to be challenging, but also quite satisfying to complete.  I think it really raises your awareness to be a safer diver, both for yourself and for others.  I devoted a three day weekend to nothing else but doing this course, and am very glad I did it.

PADI requires that you have done at least the Adventure certification (which is almost the same as the Advanced certification) before you do Rescue.  I think NAUI has a similar track.