I think the source of the issue is that Art Nouveau and Art Deco also both commonly get mixed up with Arts & Crafts (as well as Craftsman and Mission), which is

I think the source of the issue is that Art Nouveau and Art Deco also both commonly get mixed up with Arts & Crafts (as well as Craftsman and Mission), which is ancestral to them both and shares elements with both -- sinuous organic shapes and hard geometric shapes.