Both agree that the main character of Jason Bourne is a super-secret agent of the US government suffering from amnesia. He is pulled from the sea by a fishing boat in the Mediterranean, riddled with bullet wounds and carrying a bank account number in his hip. His love interest is named Marie, and she helps him recover his lost identity while trying to avoid men that are trying to kill him for what he knows.
This is where the book and the movie diverge. In the movie, Bourne's antagonists are the government agency he worked for and their team of assassins. They believe Bourne has gone crazy. The boss of Treadstone even calls him a 'malfunctioning machine.' In the novel, the government agency plays a smaller part, and in the end tries to help save Bourne's life. The real antagonist is an assassin named Carlos, a terrorist trained by the Soviets.
This divergence is interesting to me, especially since the two versions are twenty years apart. In 1980, the government was not trusted, but was not generally regarded as an evil thing, and patriotism was more popular. The movie reflects the more prevalent anti-American attitude today (especially in Hollywood), where the US government is seen as wicked and secretive. If you're curious, I much prefer the novel's viewpoint.
I enjoyed the book, and would recommend both it and the movie to those who like spy thrillers. I'm planning on reading and watching the sequels. It will be interesting to see if they exhibit the same differences.