Green onions and scallions are the same thing. Leeks are much larger. All three are members of the onion, or allium, family. Of the two, leeks have the more mild flavor.
You can slice leeks thin (wash them first, because dirt hides between the layered leaves) and saute them the other vegetables; or add them to egg salad, mashed potatoes or potato soup.
Green onions are the immature form of the onions that make us cry when we slice them. Green onions are harvested in spring, while mature onions are harvested in autumn.
You can plant the ends of leeks and green onions that have the roots. They cut ends will take root and grow, giving you a new plant you can harvest in a few months.