P&S cameras are fairly similar to video cameras, and most can capture video. The sensor can capture frames at a fairly high frame rate, and the camera "looks" at the frames to do auto-focus. The viewfinder isn't "through the lens", it's a view through a separate, dedicated, viewfinder lens.
This is an inexpensive arrangement, but AF response is slower and less accurate, and the viewfinder can suffer from parallax and doesn't demonstrate the effect of lens filters. But you do get "live preview".
On a DSLR, the image from the lens is split by a mirror/prism combo (or mirror/mirror combo on the 300D), delivering some of the light to the viewfinder and some to dedicated AF and exposure sensors. This gives you a "through the lens" viewfinder (no parallax, you see the effects of lens filters) and faster and more accurate AF sensing. But the sensor doesn't see the image until you press the shutter button, at which point that mirror flips up out of the way, the viewfinder goes dark, and the lens image is projected towards the sensor, then the shutter is opened/closed.
Most DSLRs have the ability to "lock up" the mirror, so you could move the mirror out of the way (losing the viewfinder and exposure/AF sensors), and lock open the shutter, but then again, most DSLRs don't have sensors that can provide a frame rate high enough to give a good "live preview".
Two different designs. The DSLR sacrifices live preview to gain better exposure/AF sensors and through-the-lens optical viewfinder.
-harry