The United States Department of Agriculture (USDA) regulates organic claims for food and has specific requirements that producers must follow and document. It is difficult and expensive to get certified, that is one of the reasons organic costs more.
The Food and Drug Administration (FDA) sets standards for personal care products like cleansers and moisturizers and cosmetics but they also regulate things like food labeling, pharmaceuticals for people and animals, medical devices from tongue depressors to x-ray machines, artificial organs, tobacco products, bar code scanners, and even phone apps that are related to health.
Everything on the market is supposed to follow FDA guidelines but everything on the market has not been inspected or approved by the FDA.
The FDA accepts the USDA organic seal for personal care but they have not gotten around to defining Natural.