This a guide to the marketing and labeling of food and other products.
Natural
"Natural" or "all natural" is probably the most vague and inconsistent term found on labeling. The implication is that such products have undergone minimal processing and are made with non-synthetic ingredients or materials. However, in many countries such as the US, there is no guarantee. Other countries including the UK, Canada and Israel have legal restrictions on which products can be labelled as "natural".
See: https://en.wikipedia.org/wiki/Natural_foods
Chemical-free
"Chemical-free" and "no chemicals" are phrases commonly used in the marketing and packaging of various products to promote their ingredients as natural. However, these phrases are scientifically inaccurate because all matter is composed of chemicals. A more accurate phrase would be "no synthetic chemicals". No known organization or laws define or certify lack of synthetic chemicals.
Gluten-free
Marketers have recently begun labeling products as "gluten-free" due to everything from chronic diseases to fad diets. Regulations on this label vary from country to country. Many such labels are applied to to products that typically or never contain gluten.
See: https://en.wikipedia.org/wiki/Gluten-free_diet#Regulation_and_labels
GMO
Many countries around the world require some degree of labeling of genetically-modified products. Canada and most of the US are notable exceptions. The independant organization Non-GMO Project tests and certifies food products mainly in the US and Canada. Over 70 seed companies from around the world have taken the Safe Seed Pledge.
See: https://en.wikipedia.org/wiki/Regulation_of_the_release_of_genetically_modified_organisms
Organic
Many national and international organic certification programs exist. Such certifications are typically voluntary and not legally required to label a product as organic. There are also independant labeling organizations including Oregon Tilth and Certified Naturally Grown in North America and the Wholesome Food Association in the UK.
See: https://en.wikipedia.org/wiki/Organic_certification
Biodynamic
Biodynamic certification is overseen in most parts of the world by Demeter International.