I am no optics expert but I think i can explain the scenarios you are confused about.
Essentially canon have crammed their CMOS censors into a smaller area than the 35mm back of a standard SLR (1.6 x smaller?). So, only the light rays travelling very close to parallel with each other, directly into the camera, will be represented on the final image.
A zoom lense does exactly the same thing, except it uses a lense to take a small area of light and expand it onto a 35mm back. This is why they need more light (bigger f-stop) to be used at the same shutter speed. If you pretended that the 35mm back was 70mm and the magnification was 2x then you would have the same pictures....
You are never bringing a subject closer, only by optics selecting which light rays you want to see. The rest are either out of focus or off the frame...
Does that make sense?