1. A seed is an ovule containing an embryo while a grain is a fusion of the seed coat and the fruit.
2. Typically, seeds are planted to grow plants while grains are harvested for food.
3. Grains provide food from the fruit part while seeds mainly provide food from embryo parts.
Grains provide food mainly from the fruit part, for instance, food from wheat grain is derived from the ground fruit, which is a part of the grain. In crops like millet, it is actually the seed that has properties very similar to those of the fruit part of the grains, and that is why it is handled as a grain in culinary terms.
Read more: Difference Between Seeds and Grains | Difference Between http://www.differencebetween.net/science/difference-between-seeds-and-grains/#ixzz4JWLgi8hN
Millet, quinoa, amaranth and buckwheat are described as grains, but while they are indeed granular, they are in fact seeds. The difference? I consulted my friendly agronomist, who explained that very broadly, grains contain a food source as well as the necessaries for germination. Seeds are embryonic plants.