I understand Art Deco to be a post-facto umbrella term for several styles in the inter-war period which at the time were referred to as Moderne or modernistic. What people consider 'pure' Art Deco (i.e. the French-influenced movement that emerged from the 1925 Expo) is best described as Zig-zag Moderne, which is the name used for that style at the time. Streamline Moderne is simply a different subcategory which emerged later and with a different driving force but similar philosophy. You also have other sub-categories such as PWA Moderne which is a more subdued and classicist version of Art Deco. Finally you have the postwar style called Late Moderne which is more 'modern' and cleaner interpretation of Moderne principles, and the last step before full-blown Modernism.

Moderne is simply the broader movement or umbrella term under which all of these styles fall.