Any sources for the different protection design? (I have a strong impression that both bicycling and skiing helmets are designed and tested for a very similar crash. An impact of the head with the ground, with a velocity corresponding to a fall from about head-height of a tall person. There are also helmets that are rated for both activities, but which only suit leisurely cycling for the reason underlined below. They are, however, excellent for winter cycling at a slow or a moderate pace.)

The main difference is in the need for cooling (a bicycle helmet needs to keep your head cool whilst exercising). The skiing helmet needs to keep your head warm against the windchill of going fast in the colder winter weather.

I have also a very strong impression that no bicycle helmet is designed in particular for an impact with a motor vehicle. The required test is to protect against the head hitting the solid ground from the height of an person cycling.