I think that food insecurity and hunger are two different things.
Someone is food insecure if they don't have a consistent source of food, even if they are successful in obtaining food that day.
So, if you have a child who, today, got breakfast and lunch at school, and an afternoon snack because it was someone's birthday and they brought cupcakes, and dinner at the soup kitchen at their church, they aren't hungry TODAY, but if staying home sick, or a snowstorm, or lack of busfare to church would have been enough to jeopardize that, because the family had no other means of getting food, then they're food insecure.
I actually think that food insecurity and obesity can overlap. Kids who don't know when they'll eat next have a tendency to binge eat, and families who worry about feeding their kids tomorrow may choose more high calorie foods/highly processed food when they get a chance.
Food issues in the U.S. looks different than the starvation we see in the Sudan, for example.