Onions and garlic belong to the Allium genus, in the same plant family as the lily. With approximately 750 distinctive species grown worldwide, the allium vegetables include not only onions and garlic, but also leeks, chives, scallions, and shallots.There are many different varieties of each allium vegetable.hink of your favourite savoury recipes. You would probably be hard-pressed to choose one that does not start by sauteing sautÃ©ing onions or, garlic or. Both onions and garlic belong to The allium, genus in the same plant family as the. lily