There are actually two different films based on the book Fail Safe (one from the mid 1960s and one from the year 2000). I am guessing that you want a comparison of the book and the more recent movie. (I will go ahead and tell you, though, that the difference between the 1964 film and the 2000 film is length and the deletion of many subplots as a result.) If that is not so, and you need the exact differences from the 1964 movie, please repost your question with the proper movie indicated and an eNotes Educator will answer accordingly. In short, there are more similarities than differences.
The two significant differences between the two are as follows: differences in amount of details and differences in the amount of exposition. Because of time constraints, there are many details taken out of the movie (including all subplots) that can be found in the book. One interesting detail that is changed is that, in the movie, the unidentified aircraft from Russia is eventually called an "accidental attack," while in the book it is eventually figured out that the plane was just a commercial jet that went off course due to trouble with the engine. In the novel, there is a large amount of plot exposition setting up the time period (the 1960s). White House employees wake up in the morning and go to work as it's a normal day. Others are giving tours of the White House and explaining the fail-safe system and how it works. In the movie, we are almost immediately greeted with the unidentified aircraft en route to the United States.
That being said, the similarities between the two are tremendous especially with regard to the main plot. An unidentified aircraft approaches from Russia and the six Vindicators are sent out. Vindicator Group Six mistakenly receives the attack code, and due to the Soviets jamming the system assumes they are at war. They proceed to their target: Moscow. After failing to contact Group Six, the president orders the group to be shot out of the sky so they do not annihilate Moscow. The movie and the book even talk about the decoy plane being brought down and, as a result, the one with the real bomb continues on. As the nuclear attack on Moscow is imminent, the president orders a similar attack by American planes (and using American nuclear bombs) on New York City. Even though both countries have lost a city and many people, World War III has not begun. After the American fighter drops the bombs on New York City, he kills himself.
The two also have a similar theme that can be seen in this quote from the novel:
The world is no longer man's theater. 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.
Thus, as you can see, the movie and the book have more similarities than differences. The main plot (with the exception of the exposition) is almost exactly the same. The differences are all in minor details.