De WIKI eles parecem ser a mesma coisa.
Stock versus broth
Many cooks and food writers use the terms broth and stock interchangeably. In 1974, James Beard wrote emphatically that stock, broth, and bouillon "are all the same thing".
While many draw a distinction between stock and broth, the details of the distinction often differ. One possibility is that stocks are made primarily from animal bones, as opposed to meat, and therefore contain more gelatin, giving them a thicker texture.[3] Another distinction that is sometimes made is that stock is cooked longer than broth and therefore has a more intense flavor. A third possible distinction is that stock is left unseasoned for use in other recipes, while broth is salted and otherwise seasoned and can be eaten alone.
In Britain, "broth" can refer to a soup which includes solid pieces of meat, fish, or vegetables, whereas "stock" would refer to the purely liquid base. Traditionally, according to this definition, broth contained some form of meat or fish; however, nowadays it is acceptable to refer to a strictly vegetable soup as a broth.
Uma possível diferença que um caldo é um subproduto da culinária e você faz um estoque.