I read The Bourne Identity and The Bourne Supremacy. The movies replace several main characters and even the main bad guy, Carlos the Jackal, has been left out. They never mention the past Viet Nam covert project codenamed "Medusa", where David takes on the name "Jason Bourne" after killing the original Jason Bourne.

The Bourne Supremacy movie was wildly different than the book. It takes place in China and Hong Kong. I don't remember all of the other differences or issues other than the books feel dated with much older technology. The films are really entertaining. The stories are almost completely re-written, however.