Please keep in mind that there were two films made from the Fail Safe novel. One was made in 1964 and one was made in 2000. I am assuming you are speaking about the more recent film. If that is not so, please repost your question and an eNotes Educator will compare to the earlier film.
The film and the movie have more similarities than differences, especially with regard to theme and plot. The major theme of both is the threat of nuclear war and the problems nuclear war creates. The irony that nothing in nuclear war is "fail safe" permeates both the novel and the film. This is very well stated here in the novel:
Man has been made into a helpless spectator. The two evil forces he has created—science and the state—have combined into one monstrous body. We're at the mercy of our monster.
In addition to the theme, the plot is almost exactly the same (as long as we skip the exposition and subplots). An aircraft approaches from the USSR and the "fail safe" system is put into effect: the six Vindicators are sent to their fail safe targets. Vindicator Group Six, due to a technical malfunction, mistakenly receives the signal to go on to its destination: Moscow. All the other Vindicator groups are called back safely. Because Vindicator Group Six cannot be reached and is about to start a nuclear war by bombing Moscow, the president orders the group to be shot down. A group of aircraft is deployed, but they fail to shoot all of them down. Even though they shoot down the decoy planes, they fail to shoot the ones with the real bombs. America's bombing of Moscow is now imminent. In order to prevent World War III, the president orders his own forces to drop nukes on New York City in order to counteract the failure of the fail safe system. The pilot does so and then kills himself.
Despite the similarities, the movie and the book have differences, too. The biggest difference is that the movie has almost no exposition! The movie cuts right to the chase and shows the unidentified aircraft from Russia. The book begins with White House employees starting their day like any other: tours go on, security is held fast, etc. It is during one of the tours of the fail safe room that it goes to "Code Blue." The second difference is one of detail. Movies, because they are shorter, must contain less detail than books. This movie is no exception. Every subplot ended up on the cutting room floor. The most interesting detail that is changed, in my opinion, is that the movie calls the unidentified aircraft from Russia an "accidental attack" while the book shows it is simply a commercial jet with engine trouble.