Both the Art Nouveau and Art Deco movements emerged as reactions to major world events; the Industrial Revolution and World War I, respectively. While both embraced modernist elements, they're easy to distinguish if you know what to look for.
Art Nouveau means "new art," and reigned from roughly 1880 until just before World War I. Art Nouveau embraced Europe's new industrial aesthetic rather than challenging it. It features naturalistic but stylized forms, often combined with more geometric shapes, particularly arcs, parabolas, and semicircles, The movement brought in natural forms that had often been overlooked like insects, weeds, even mythical faeries, as evidenced by Lalique jewelry or Tiffany lamps.
Art Deco, on the other hand, emerged after World War I. In fact, the deprivations of the Great War years gave way to a whole new opulence and extravagance that defined the Jazz Age and the Art Deco aesthetic. The movement, prevalent from the 1920s until roughly the start of World War II, took its name from the 1925 Exposition Internationales des Arts Décoratifs et Industriels Modernes held in France and is characterized by streamlined and geometric shapes. It also utilized modern materials like chrome, stainless steel, and inlaid wood. Deco features bold shapes like sunbursts and zigzags and broad curves. If you check out the spire of the Chrysler Building, the hotels of Miami's South Beach, or the "coffin nose" oif a 1935 Cord Model 810, you'll be staring at the very definition of Deco.