Grains are specifically the seeds from different types of grasses. Find some pictures of wheat, rice, oats, and even corn plants, and you'll notice they look similar to the grass that grows tall in unmowed fields. The word "vegetable" does not have such a precise meaning, but it usually refers to non-sweet tasting edible plant parts. Many things that are called "vegetables" are actually fruits (the ripened ovary of a plant) such as tomatoes and squash. However, grass seeds are usually called "grains" not "vegetables" (although some people call corn a vegetable and some people call it a grain). In my opinion, it could be considered as a vegetable, but different people will use the word vegetable differently.