Functional food contains an added ingerdient, not normally found in that food.
Differences between prebiotic and probiotic food
Prebiotics contain added sugar called OLIGOSACCHARIDES. When we eat these foods the sugars are not digested by the body but are food for the 'good bacteria' in our gut. The 'good bacteria' increase in numbers. 'Bad bacteria' and humans cannot digest the prebiotic - they do not have the right enzymes. Prebiotics naturally occur in foods like leeks, onions and oats, but you cannot get enough of them in a normal diet to cause a significant effect. This is why some people take supplements. Prebiotics are not produced by fermentation.
Probotics contain the 'good bacteria' themselves. When we eat these foods, the bacteria lost because of poor diet, stress and so on, are replaced. Probiotics are produced by fermentation, when bacteria ferment milk and other foods.