A wise man once said that when you boil it down, there are two types of story. The “quest” and the “chase.”
the quest story
The quest is a story in which your protagonist has an aim and must go on a journey (literal or figurative) to achieve that aim. She sets off from home. He heads off into the bad country. They take on their enemies to achieve the inner sanctum and carries home the prize.
But your protagonist is going to come up against some serious obstacles. There will be people who want to stop her achieving what he wants to achieve. More importantly, there will be obstacles that originate within your protagonist themselves. Whether it is fear or weakness, or just uncertainty, they will have to overcome their own flaws to achieve what they want most of all.
There are a whole variety of stories that fall into this category: think Indiana Jones going after the ark of the covenant, or Clarice Starling searching for the identity of Buffalo Bill, or the Hoover family trying to get to the Little Miss Sunshine beauty pageant.
The beauty of these types of story is that they allow your protagonist to have clear wants and desires and they allow your protagonist to develop over the course of your story. Nothing makes you change like a journey, nothing drives your character forward like the hope of achieving the object of their quest.
the chase story
Then there are stories in which your protagonist is happy, but is jolted out of their complacency by something unexpected. Maybe something dangerous. An inciting incident will put them in peril and they will be forced to get out of it. They will, inevitably, go on the run.
These can be thrilling and exciting stories. They are examples of direct and compelling narratives. The stakes are high, the conflict is clear and concise (the battle between the pursuer and the pursued) and the character ambition is clear (to survive or escape). If you write a “chase” story, however, you have to ensure your character isn’t too passive. You want your main character to do something, to want something, and then to go out and do it.
That’s why even in films structured as a chase, you’ll often see that in the second half of the film the aim of the character moves from simply surviving to trying to strike back.