Well it depends on what you mean by ‘crash helmet’ and ‘ordinary helmet’ really. There are hundreds of different types of helmets and they all provide different sorts of protection. Crash helmet is a generic term for any sort of helmet designed to protect your head in a crash. Cycle helmets are crash helmets, as are Motorcycle helmets, and all the various forms of helmets used in four-wheeled motorsports.
If you’re talking specifically about the helmets used in F1, and how they’re different from helmets in other motorsports, then there are a few key things. Basically they’re a full-face helmet which conforms to the highest safety requirements. They would be eligible for use in lower series as well, but may not meet the other demands of other forms of motorsport. There’s nothing specifically which is unique about an F1 helmet, it just features all of the safety features that are available. There’s a decent article on the F1 site about them – http://www.formula1.com/inside_f1/safety/helmets_hans_clothing/7438.html
The thing that article doesn’t mention is the mounting points for the HANS device, which prevents the driver’s head being thrown forwards or sideways and damaging his neck.
The difference between a motorcycle (crash)helmet and a helmet for racecars (and karts) is the size of the chin protection and the size of the ‘open space’ for your eyes to see through. In cars and karts, the protection of the chin is more important than for motorcycles. This part is bigger and goes to the expense of more periphiral vision (well up and down maybe, which is for motorcycles much more important than in cars/karts).
It’s difficult for me to explain in English (which is not my native language), but I hope I made it clear.