Difference between shallot, onion, leek, and garlic plants

Q: What is the difference between shallot, onion, leek, and garlic plants?

A: I am told that a good cook would be able to identify onions, leeks, garlic and shallots simply by tasting the leaves. That leaves me out!

For me, the shape of the roots is key. Onions typically have the round bulb shape we all recognize. Garlic has a bulb with several cloves. Shallot roots are swollen, but oval, sort of like a fig. Leek roots don’t swell much at all; the base and roots are club-shaped. Leek leaves are recognizable but hard to describe. They are blue-green and have an opposite and overlapping shape.

Here’s a good photo: