There are two categories of dry onions, storage onions which include the yellow, white, red onions, and shallots. These onions contain a higher amount of sulfur and are lower in moisture and can be stored in a cool dry location for long periods of time.
The other category is sweet onions which contain less water and sulfur like. These sweet onions include Vidalia, Maui, and Walla Walla. These onions are only available a few months of the year from April to August and don't store well for long periods of time.
Storage onions are typically cooked whereas sweet onions may be eaten raw in salads and other dishes.
Green onions are simply immature onions. Green onions are the most perishable of all the onions and can be eaten raw or cooked.