I think the analogy is entirely apt.
If there is no confusion then why is a Presidential Candidate able to say “The war on terror is a bumper sticker”?
In one sense, you're right, the analogy is perfect, as a construct of words. The problem is that its perfection is not reflected in reality. There is a real-life analogy that holds up very well: Roosevelt (eventually) attacked the Japanese, and President Bush drove the Taliban and Saddam out of power. Bush also had other terrorist leaders blown up by killer drones, and pursued Islamist networks of cash and communications all over the world. He hasn't been sitting on his hands.
why is a Presidential Candidate able to say “The war on terror is a bumper sticker”?
A candidate for President is liable to say anything. If Bush had declared war on Saudi Arabia, it would still be derided as a bumper sticker by someone.