A long question !
With some research, these seem all to be related (but different) plants in the Genus Allium. Some of the names that you list are just the same plant in a different area .
Lists of different plants
- Chive - this is a herb used in cooking, usually the smaller leaves are used.
- garlic chives, Chinese chives, Oriental garlic, Chinese leek, also known by the Chinese name kow choi. All names for the same thing. You should know this one.
- leek. These are quite big. Say the thickness of 2 fingers at least.
= Scallion = green onion = spring onion. Also called shallots. Usually used in cooking, chopped up, bigger than a chive, smaller than a leek.
However all the names that you listed are common names, so depending on where you are, a person might use the same name for different things. I have tried to group them in commoner categories.