Since you probably haven't seen the 1994 movie, let's go through a quick summary. The movie follows the origin of the Fantastic Four, which in this incarnation results from a mysterious cosmic energy called Colossus. The mission to study Colossus fails because a thief known as The Jeweler swaps out a diamond critical to the equipment. The fake diamond can't to contain the power of Colossus, and Reed Richards, Ben Grimm and Sue and Johnny Storm are engulfed in the energy that turns them into the Fantastic Four.
The film also features Victor von Doom as the primary villain. Doom's origin is similar to the heroes -- in college he tries to harness Colossus' power, but his machinery fails and he is apparently electrocuted. Unbeknownst to our heroes, Doom survives the accident and is whisked away to his homeland, Latveria. There he re-invents himself as Doctor Doom and plots his next attempt to capture the power of Colossus. He wants Reed's diamond for his own, so he retrieves the diamond from The Jeweler and prepares to tap into Colossus and dominate the world.
The Fantastic Four confront Doom in his castle. They manage to destroy Doom's equipment and foil his plans for world domination. After a fight with Reed Richards, Doom clings to a balcony on his castle, dangling over a deep chasm. Reed tries to save Doom, but Doom slips out of his gauntlet, seemingly falling to his demise. The heroes return home, and shortly afterwards Reed and Sue are married.
Now that you know a little about the 1994 film, we'll move on to the comparison to the 2005 movie and the comic books.