If one asks, "Why are they different?" that's the first step in a journey to a destination of understanding that exposure is not the same as the total light used to make a photo.
Different format camera can work with the same f-stop and same exposure (the same scene brightness per unit area of the sensor) but that does not guarantee those cameras will make the same photo. In fact, it pretty much guarantees the opposite. The photos will be different...potentially significantly so to the eye. At the same exposure, a smaller format camera captures less total light and makes a photo having more prominent shot noise. At the same f-stop but with different focal lengths, a smaller format camera at a shorter focal length will be working with a smaller diameter lens aperture. Depth of field in the resulting photo will probably be greater.
Equivalence helps a photographer understand those differences and how to use a camera of any format to make the photo they're envisioning.