No. Corn is a grain grown on a type of grass. Wheat, rice, barley and oats are also grains that grow on different species of grass. Bamboo is a type of grass and so is sugar cane.
Fruits have a fleshy coating with seeds inside. Strawberries are a fruit with a fleshy coating but the seeds grow on the outside of the fruit.
Vegetables have a flower stalk and produce seeds on the flower stalk. Vegetables fall into 2 main categories, leafy and root vegetables.
1) Carrots, onions, leeks, garlic, beetroot, sweet potatoe, normal potatoe, parsnips and turnips are all types of root vegetable.
2) Lettuce, spinach, silverbeet are leafy vegetables. Cabbage, cauliflour broccoli and brussel spounts are also leafy vegetables.
Peas, beans and peanuts are legumes and produce a seed pod with a few seeds in. Legumes take nitrogen from the atmosphere and have special roots that put the nitrogen into the soil.