From a purely legal perspective, organic is certified by a government regulatory body and natural is not. Organic food fans want their food to be completely free of chemical fertilizers, pesticides and preservatives. Natural food folk believe that synthesizing a food item results in loss of nutrients and other healthy properties, so they want natural foods.
The United States Department of Agriculture is the domestic certifying body for organic food. The Organic Food Products Act defines the rules and parameters for food items that are produced, manufactured and handled organically.
Here are the practical differences:
Of, marked by, or involving the use of fertilizers or pesticides that are strictly of animal or vegetable origin: organic vegetables; an organic farm. Raised or conducted without the use of drugs, hormones, or synthetic chemicals: organic chicken; organic cattle farming.
Free of artificial or synthetic ingredients or additives, including color, flavor or any ingredient “not normally expected.” Hence, lemonade flavored with beet juice cannot be called natural.