Program vs. Auto Modes
Your camera's Program and Auto modes are clearly different--for one thing, camera manufacturers are unlikely to create two modes that do the exact same thing. Here's a typical camera settings dial, where you can see Auto, P (Program), S (shutter priority), A (Aperture priority), N (Manual mode), and others.
Camera models may vary, but in general, Auto truly means "automatic." When you dial in "Auto," your camera takes care of pretty much everything except where you point the camera and how much you choose to zoom. The flash, ISO (which is the camera's sensitivity to light), white balance, shutter speed, and aperture are all set automatically.
Program mode (sometimes referred to as the "Programmed Exposure" or "Programmed Automatic" mode) is a bit more flexible. When you dial in the P, the camera might look like it's in the same sort of autopilot mode as Auto, but you have full control over a surprising number of settings, including ISO and white balance, which are unavailable to you in Auto.
For example, you can crank up the ISO higher than the camera might ordinarily choose in order to freeze the action in extremely low-light situations. Or you might keep the ISO low to minimize digital noise. If you want to get motion blur or light trails at sunset, Auto mode will generally make that impossible because the camera will increase the ISO automatically. In Program mode, you dial in the right setting depending upon the situation.