Yes, they are different. When left in the garden, many regular leeks will form little bulbils on the outside of the root. When the mother plant dies, the bulbils grow and form a clump. But all this is very slow, so you get better production by growing regular leeks from seed.

Perennial leeks enthusiastically form little bulbs in clusters, kind of like little shallots, only with two very long green seasons and a short midsummer dormancy. Southern Exposure sells them but they are out for the year.