G. Gershwin 3 preludes

[eduardom]

Is Gershwin's music considered as jazz music? For example his preludes.

And if so, what are the main differences between classical music and jazz music?

[indianajo]

Gershwin heard jazz in clubs, and was heavily influenced by it.  He never developed a skill for improvising on the spot on classic melodies, so most true jazz musicians disdane the reputation he has for being a "jazz" musician. 
Gershwin was professionally in his youth, a "song plugger" for tin pan alley, the sheet music business, and out grew the limits of that profession. 
You should watch PBS-TV more, this has been covered a lot.