Barley is not a wheat. It's a cereal *grass*, but not a cereal *wheat*.
They're different species (Hordeum Vulgare vs Triticum Annuum), each in a different genus (Hordeum vs Triticum). They are in the same family, Poaceae, and the same tribe, Triticeae within that family.
I'm guessing you're asking due to gluten concerns? Wheat, Rye, and Barley all contain gluten, although wheat has much more than the others.