Difference between natural and organic

Natural is purely a marketing term, and it is essentially meaningless since it isn't regulated by the USDA (I'm assuming you are in the USA, I can't speak for other countries). Since the term isn't regulated (with the apparent exception of meat), any manufacturer can put it on any (non-meat) product that they want, whether it is actually "natural" or not.

Organic is well-defined by the USDA and places a number of restrictions on the types of pesticides and other chemicals that can be used to grow the crop. For things like meat, the organic label regulates both the drugs that the animal is given as well as the production of the feed.

Certified organic food products are regulated by the U.S. Department of Agriculture and produced by farmers and manufacturers under a strict set of rules. But the agency defines the term "natural" only for meat and poultry. In the rest of the food industry, the meaning is largely up to the producer.

See: http://articles.chicagotribune.com/2009-07-10/business/chi-natural-foods-10-jul10_1_organics-or-least-chip-popular-horizon-organic-brand-organic-industry-watchdog-group

Natural "Natural foods" and "all natural foods" are widely used terms in food labeling and marketing with a variety of definitions, some of which are vague. The term is assumed to imply foods that are minimally processed and do not contain manufactured ingredients, but the lack of standards in some jurisdictions means that the term assures nothing. The term "organic" has similar implications and has an established legal definition in many countries and an international standard. In some places, the term "natural" is defined and enforced. In others, such as the United States, it has no meaning.

Organic Organic foods are those that are produced using environmentally sound methods that do not involve modern synthetic inputs such as pesticides and chemical fertilizers, do not contain genetically modified organisms, and are not processed using irradiation, industrial solvents, or chemical food additives.

(Information from Wikipedia)

From http://www.organicfacts.net/organic-food/organic-food-basics/difference-between-organic-and-natural-food.html

Organic food refers to food items that are produced, manufactured and handled using organic means defined by certifying bodies such as the United States Department of Agriculture (USDA) under its Organic Food Products Act. Natural food, on the other hand, generally refers to food items that are not altered chemically or synthesized in any form. These are derived from plants and animals. Thus a natural food item is not necessarily organic and vice versa.

as far as I understand it, there's really no clear definition to either of these two terms and they're mostly overused by companies to sell you products. I believe the use of "Natural" is a little more devious. For instance, I just bought some "Natural Style" apple juice the other day. I'm sure it's just as processed and pasteurized, it's just a slightly different flavor/color.