Maize is a member of the monocots, and broad bean is a dicot plant. There are many structural differences between moncots and dicots, including critical differences in the seeds.
The most obvious difference, and the one for which the groups are named, is the number of cotyledons. Monocots have one cotyledon, or seed leaf, which dicots have two. Additionally, the cotyledons themselves are quite different between the two groups.
During development the cotyledons of dicots like beans absorb the endosperm within the seed and convert it into starch, which is stored inside the cotyledons. In maize the endosperm remains in its original location packed around the embryonic plant, and is not absorbed for nutrition until the seed starts to sprout.
Once the seeds begin to sprout, the bean's cotyledons will emerge attached to the stem, functioning as the plant's first leaves. The seed coat, which is not well attached to the rest of the seed, will split and fall away. Even as the stored starch is being withdrawn from the cotyledons to help the plant begin to grow, the cotyledons will begin to perform photosynthesis.
In maize, the cotyledon will emerge in the form of a coleoptile, a protective cap covering the plumule, or shoot. The coleoptile is surrounded by a sheath called the scutellum, an organ which is adapted to absorb the endosperm and pass its energy to the growing shoot. In maize, the seed coat, which is firmly attached to the underlying endosperm, will stay in place and shrink as the endosperm is used up. In maize, the shrunken remnant of the seed will remain attached to the plant stem just below the surface of the soil, whereas in the bean the entire seed (except for the seed coat) actually becomes the plant.