In intense situations, a person's instinctual reaction causes him/her to react, whether it means taking flight and running or taking a stand and fighting what is coming.
Henry, in the Red Badge of Courage, runs for his life. When the battle that his unit is about to fight seems as if there is no way they will win, he abandons the rest of his "brothers" in his unit. Leaving them to fend for themselves. This tells the reader that Henry is only thinking of ways he can save himself.
Forest, in the movie Forest Gump, runs because his lieutenant orders him to. However, as he turns and realizes that the rest of his regiment is in trouble, he turns back and helps out even though he is putting his own life in harms way. In other words, Forest is thinking of ways he can help others, not just himself.
The above character foil further illustrates that people run for varies reasons.
