Use of the term "organic" is regulated by the federal government. Federal standards prohibit the use of synthetic pesticides, herbicides, fungicides and the use of chemical- or sewage sludge-based fertilizers on or around crops. Certifying agencies must be USDA-accredited.
The term "sustainable" does not have a legal definition, but refers to a range of agricultural practices that are ecologically sound, economically viable and socially responsible. Sustainable farmers can choose what works best for their property and generally recycle, conserve energy and water and use renewable resources when possible. They might choose to use cover crops and compost to add nutrients to soil. They might control pests with native birds and beneficial insects. And, if they need chemicals, they'll choose the least toxic option. Regional and local certifying bodies exist.
"Biodynamic" is also not legally defined. Some say there are 4 key principles. All organic waste must be recycled. A diverse population of predator and prey animals, birds and insects must be encouraged to maintain ecosystem balance. Preparations such as diluted treatments and composts made from herbs, minerals and manures are applied to the land to promote crop fertility and control pests. Finally, landowners must recognize the interrelationships among everything on the farm and understand that nothing is optional and all is in pari passu. The Demeter Association is the international biodynamics certifying body.