Rivalry and underdog plots are similar. An underdog plot is always a rivalry plot, in fact, but a rivalry plot is not necessarily an underdog plot.
In both story lines there is competition between the protagonist and the antagonist. In an underdog plot, the hero is in a diminished circumstance, in some way lower than the antagonist. For example, in the classic movie "Rocky" the hero is clearly on a much lower level in boxing than Apollo Creed the champion fighter who challenges the "local boy" to a legitimate boxing match.
In a straight "rivalry" plot, the foes are on a level plain. They may have different skills which they will employ in the competition, but they are equal as competitors on the whole. The sequels to "Rocky" are rivalry stories rather than underdog story lines because, in the end of the first movie, the hero has raised his status to the same level of other boxing champions.
The competition in a rivalry or an underdog plot may be an actual contest like a boxing match, bowling competition or a bake off, but it can also be a competition for something less tangible.
For example, every version of "Cinderella" is an underdog story, and the competition is always about love and marriage. The movie "The Patriot" starring Mel Gibson is in many ways a rivalry story with the competition being between the British soldier who shot the American farmer's son and the American farmer (Gibson). The two main characters in this movie, though in different circumstances, are on an equal playing field.
In both rivalry and underdog story lines the protagonists and antagonists are fighting for the same thing. (Apollo Creed and Rocky want to win the boxing match. The British soldier and the American farmer want to win control of the United States, either for Britain or for America.)
Both kinds of stories have three essential stages, much like other types of plots.
In the first stage of rivalry and underdog stories the hero and villain are living their normal lives when the antagonist instigates something which challenges the protagonist. In the beginning phase of the story the antagonist gets the upper hand which leads the protagonist to react and prepare for the competition which will begin in the second stage of the story.
The second stage of the rivalry and underdog plot is all about the rising and descending power of the two main characters. Though the protagonist usually takes quite a beating during this phase of the story, he does enjoy a few victories.
The third stage brings the showdown between the villain and the hero. This is the grand competition. Everything which has happened up to this point has led to this confrontation. Rocky has spent all of his time training for the fight. The American farmer has sacrificed everything and, at last, faces the man who murdered his son and wants to take away the freedom of his countrymen.
Once the competition is over in a rivalry story, everything in the protagonist's world returns to normal. In the case of the underdog story line, the hero may or may not win the competition, but the reader should be given a satisfying ending. Rocky didn't win, but he wasn't clearly defeated either, and people who saw the movie walked away satisfied with the ending (satisfied enough to inspire LOTS of sequels).
Competition is always seductive to the observer, whether we're attending a sporting event, reading a book, watching a movie or frittering away a little free time watching a reality show on television.
We like competition. That's probably why a well written rivalry story (and underdog story) is always popular with Readers.
Fran Shaff, Award-Winning Author
Fran's Web Page