That ski helmet appears to be an uvex wing rc (or similar). The first cycling helmet appears to be a Kask Mojito variant. Note that both companies make both kinds of helmets.
- Mostly constructed of crushable foam
- An outer shell that will slip across surfaces in a collision
- Fit adjustment systems
- Moderately aerodynamic design
- Ski helmet's shell is harder
- Ski helmet has much less ventilation (it's on the top, where not visible in y our picture)
- Ski helmet's ventilation can be closed down
- Bicycle helmet is lighter (220g vs 490g)
- Ski helmet covers ears
- Ski helmet is designed to work well with ski goggles
- Ski helmet has mount points for a chin guard
The ear coverage and ventilation differences have a pretty obvious reason. Skiing is done in sub-freezing temperatures and for a much shorter duration of time than a road race. It's important while skiing downhill to keep warm and to keep the ears covered, but with road cycling it's more desirable to maximize ventilation. Watching the other outdoor winter olympic sports, the cross-country skiers have a band covering the ears, and almost everybody else has a hat, balaclava and/or helmet so that their ears are covered.
Road racing cyclists do everything they can to keep weight down because it helps with climbing and acceleration. Also, the position of the rider and length of a road race means that any extra weight can make the neck tired. Downhill skiers are pulled down by gravity and have a more head-supporting upright posture, so a tiny bit of extra weight won't make a difference.
I believe the shell hardness difference really has 3 reasons. First, skiing downhill has a greater chance of multiple head impacts from a single crash than cycling does. Second, weight. Third, hard shells make ventilation trickier.
As for the time-trial helmet: The regular cycling helmet is made for cycling in a pack for 4 hours. The time trial helmet is made for cycling alone for a much shorter time. There's still ventilation on most time trial helmets, but it's subtle. Aerodynamics are important for both kinds of cycling, but a lot more important in that time trial, since there's never anybody to draft behind. Ventilation is still important for both kinds of racing, but more important for the longer rides, since heat and discomfort will build up over time. And, to top it off, there are regulations about the helmets that I believe wouldn't allow the time-trial helmet in a road race.