According to Disney Dining, the official policy is that 3-9 is considered a child and 10 years old and up is considered an adult just like with the parkhopper passes.
When I made all my Priority Seatings they asked the ages of my children and I told them that my daughter was nine but would be turning ten during the trip.
When we went to Blue Bayou and the Carnation Cafe, they did not ask my daughter her age and although she was wearing her birthday badge that clearly stated that she was celebrating her 10th birthday, I ordered from the children's menu and there was no problem.
However, when we went to Goofy's Kitchen, we were asked her age and she was charged for an adult meal.
My understanding is that the official policy is that for all meals, a child is considered 3-9 but in our limited experience, only the character meals enforced this policy.