GREEN ONION/SPRING ONION
You might think you know that green onions are called spring onions, but is there really a difference?
If you are familiar with green onions, you should be familiar with spring onions and scallions. That's because these are all the same thing just with different names. Allium fistulosum or the green onion is literally the young stalk of an onion. The green onion stalks, complete with the bulbs, can be harvested from either young white or red onions. The bulbs won't develop and show their white and red varieties until it's a more mature plant.
LEEK
Leeks are not green onions. While both are considered part of the onion family, these are two different herbs. Known scientifically as Allium porrum, the leek looks like a large green onion stalk. Even the young and thinner leeks are much bigger than green onions would be.
Besides the size there is a considerable difference in the way leeks grow compared to the green onions. You'll notice that leeks develop a distinctive fork as the plant grows from bulb to its leaves.
CHIVES
Chives are actually another kind of plant altogether from the green onions and the leeks. It has a different scientific name (Allium schoenoprasum) . Most of the Alliums are bulb-forming except Allium schoenoprasum (common chive) that grows from rhizomes. Chives are sometimes called "onion chives" because that's what chives tastes like. However, it's not a green onion.
There are actually two kinds of "chives" you might find in the market: chives (Onion Chives) and garlic chives or Chinese chives. You might sometimes be fooled into buying garlic chives instead of real chives.
How can you tell which is which?
If you look at the plant itself, the green leaf blades of the garlic chives are flat compared to the real chives which are hollow and circular. The stalk of the chives is also much smaller, thinner, and much greener throughout the stalk than the stalks of the green onions or even the garlic chive. You can tell chives apart from the garlic plants as well as from the flower buds these sometimes have. If you allow the buds to flower, chives sport purple flowers while garlic chives will have white flowers.
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Reference
Plants of Singapore