The major difference between Beans and Seeds is one of classification. All Beans are Seeds, but not all Seeds are Beans.
Seeds can vary from the hard pit of a Peach, Olive or Avocado to the soft seeds of a Tomato or Corn to the soft and hard seed of the Pomegranate. Seeds are the complete reproductive material of a plant.
Beans are a specific variant of Seed, one that grows in a husk in a pod that splits down both sides. Beans are found in among the following Legumes: Pea (Pisum Family), Legume (Fabaceae Family ), Lentil (Lens Family), Hyacinth (Lablab Family), Soybean (Glycine Family) or Coral Bean (Erythrina Family).
Other vegetables and plants grow similar types of seeds and pods, though they are technically not legumes and therefore not capable, technically, of producing beans. Examples of faux beans include: Coco Beans, Coffee Beans, Vanilla Beans and Castor Beans.