Yes ReyeR always seems to know that little bit more than me but i'll give it a stab. ReyeR tune in and fill in the details.
As others have said part of the lag in speed it due to slower processer and autofocus, exposure calculations, etc, etc. However this can be almost eliminated by half pressing the shutter button. All these things are now taken care of. The part that I consider to be actual shutter lag is the time taken after all these calculations are done to actually take the picture. A compact digicam does not work like a normal film camera, ie exposing film. To see the picture on your LCD you must already be exposing the CCD to light and are actually seeing what the CCD is seeing. When we want to take a snap the LCD must 'freeze' for a period of time and clear the charged couples for actual exposure like MacHealth said. This takes a finite amount of time, hence no digicam can ever have no lag because of this. (A70 only is about 0.15ms for this to occur, which is faster than most and why I like it).
A DSLR is not the same. They still work lke the film counterpart, with a mirror. The mirror flips up same as film when the shutter is clicked and the CCD is only exposed for the correct time, etc. This answers your question I think.