Spring onion  = scallion = bunching onion = shallot (in Australia) = Green onion (West) = Chinese onion = stone leek = cibol = Qing Cong (Mandarin) = Ts'ung (Cantonese) = Negi (Japanese)

Spring onions have been cultivated in China and Japan since time immemorial. These are onions that have small white onion bulbs and long green stalks. Some people also use the term green onions to refer to onion tops, shallot tops and young leeks.

Spring onions have a more subtle smell than onions and the taste can vary from fairly mild to really pungent. Smaller bulbs generally have a milder flavor.

In Asia, spring onions are served as a vegetables as well as being used as a flavoring agent. They're usually eaten raw, but you can also grill or sauté them.

Chinese Chives = garlic chives = ku chai = Jiucai (Mandarin) = Gau Choi (Cantonese) = flowering chives = flowering Chinese chives = flowering garlic chives

Although they belong to the same family, Chinese chives are quite different from the Western variety, both in their appearance and taste. Two species are available: one has long, flat green leaves like a small, thin leek, the other has long, tubular stalks with a single bud at the tip.

Chinese chives have a much stronger aroma than the ones grown in the West. They don't really taste of onions, but have a flavor that resembles a cross between garlic and leek.

Chinese chives are seldom used as a garnish, but are either served as a vegetable in their own right, or used as an ingredient in cooked dishes, especially with seafood or meat. A very popular Chinese vegetarian dish features chopped chives cooked with scrambled eggs and bean curd. This is not only colorful, but taste delicious.

Sweet onion = fresh onion = spring onion = summer onion = Yang cong (Mandarin) = Yun Ts'ung (Cantonese)

There are several different varieties, often named after the region in which they're grown. They're usually available from March through August, though some producers extend the season by storing them in a low-oxygen environment.  Sweet onions are usually larger than storage onions.  They also have a higher water content, so they don't keep as well. 

These onions are mild and crisp, so they're the onions of choice for slicing raw on burgers and sandwiches. They can be lightly cooked, too, though they're not as pungent and flavorful as storage onions. 

Yellow onion = yellow globe onion = yellow storage onion

This is what most cooks reach for when a recipe simply calls for "onion."  It's higher in sulfur than the white onion, so it has a more complex flavor.  The sulfur, unfortunately, is also what makes you cry when you cut into it. 

Yellow onions turn a rich brown and become sweeter and milder when cooked.  Many people find them too pungent to eat raw. The onion is a very versatile vegetable. It can be eaten fried, boiled, steamed and it is an essential component of a great number of sauces and dishes, such as curries and stews. Fried onions are a popular garnish, especially in South-east Asia.

Red onion

These are sweet enough to eat raw, and they're often used to add color to salads.  They're also excellent grilled or lightly cooked.
 

Shallot = Fen cong (Mandarin) = Ts'ung tau (Cantonese) = Hom Daeng (Thai)

Although they belong to the same family as garlic, leeks, chives and onions - and look suspiciously like baby onions - shallots are very much their own vegetable. Sometimes called bunching onions, they have bulbs that multiply to produce clusters joined at the root end.

Shallots tend to be sweeter and much milder than large onions. They have a more delicate, garlicky flavor than other cooking onions, and are a common ingredient in French sauces. Some Thai varieties are sweet enough to be used in desserts.

Indispensable in South-east Asian kitchens, shallots are far more popular than both regular onions and spring onions for everyday use. Minced with garlic, ginger and other aromatics, shallots form the standard marinade and are also an essential ingredients in curry pastes and satay sauce. Dried shallots (hanh huong) are a popular alternative in Vietnam.