The term of art is terroir [1], which is the "character" of the environment the plants are grown in. It's often that a region will have some special characteristic due to geology that allows a unique flavor profile to grow so these trade names are the equivalent of a terroir brand.
Some designations are more strict than others, though. IIRC in the case of Vidalia onions the soil is low in sulfur so the biochemical pathways in onions that produce astringent compounds are nutrient starved. As far as I know most sweet onion varieties nowadays are grown in similar soil, but they're not legally allowed to call them Vidalias.
