Both healthy and healthful are used to describe food that is believed to be good for your health, but healthy is by far the more common choice in the phrase healthy food.
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Since the late 1800s, usage commentators have been telling English speakers that only healthful can be used to mean "beneficial to health of body or mind" or "good for your health," but this is simply not true; healthy has been used in this way since the middle of the 16th century. In short, then, both "healthful food" and "healthy food" are correct, but "healthy food" is by far the more common collocation, even in published, edited text.
As for health food, this term actually functions as a compound noun with a somewhat more specific meaning than "healthy/healthful food." It's much more common than either healthy food or healthful food in English.
Health food is defined in Merriam-Webster's Advanced Learner's Dictionary, as follows:
: a food that is believed to be good for your health : a food that has no artificial ingredients
- He eats only health food.
- She shops at the health-food store.
- The restaurant offers a variety of health foods.
