Good question and the answer really comes down to can you trust what the produce section labled things. For your just regular ole onions and green onions buy them from your favorite grocer. Some of these others I would actually go to a "farmers Market" type thing. Most larger citiies have them.
Here in the USA your basic onions are again those white, red or traditional called yellow covered those aleady. They do fine served raw as in a sandwich, or cooked with, or as a topping.
Green Onions: are best used as a topping. They are much milder. When cooking with them they are best added to the last part of the recipe as they break down easily. The scallion confusion is most likely a country diference, they are really the same thing.
Leeks: Looks like a green onion that really went wild in the growth process. It is a different onion. The taste is similar to a green onion. They are much tougher so I would not use them as a fresh topping. They are great in soups, stews, or stocks.
Shallots: Probably the most confused thing there is when it comes to onions. A true shallot is grown in Asia, Australia also has there own variety. They should resemble more of a garlic type clove appearance (oblong in clusters as opposed to a bulb). They should still have a natural outer skin just less of one that we are used to seeing. They are packed with flavor, and also packed with an expensive price tag. These are best to cook with and not as a fresh topping the flavor is just to overwhelming when served fresh.
The closest thing in the USA to a shallot is a baby onion. They are not the same and usually not worth the added expense. They like their cousin they tried to copy are a bit more powerful and best to cook with, if you decide to buy them.
Be careful with what you buy and what some are passing off as something they are not. I could take a leek for example cut off all the green parts and call it a shallot.
Hope this helps