Welsh Onions are Allium fistulosum (Alliaceae). They are also known as green onions, bunching onions and scallions, but those terms refer more to function than taxonomy and can include some types of garden onion (Allium cepa) or shallots. Welsh Onions never form a solid bulb and the scape is hollow and fragile, very like the leaves. Besides their use as green onions in cooking, they are often grown in a bunch as a foliage ornamental perennial.

A good image of welsh onion in flower can be found here.