What's the difference between neoclassical and art deco style in architecture?

I've seen buildings of both styles around cities and the difference really jumps out at you. Neoclassical (18th-19th century) is all clean lines, Greek columns, rigid symmetry and inspiration from classical antiquity, very restrained and "noble." Art deco on the other hand (1920s-30s) is much more decorative and geometric, with angular forms, stylized motifs, luxurious materials and a more modern, urban vibe, almost futuristic. Basically neoclassical looks back to ancient times, while art deco celebrates the progress and modernity of its era.

What they say about neoclassical symmetry is right, but in my opinion they underestimate how neoclassical was also kind of cold and academic, whereas art deco (1920s-30s) is pretty much the opposite: elegant sure, but with curves, abstract geometries, and decorations that explode everywhere. Neoclassical looks back to ancient Greeks and Romans, art deco is futuristic and celebrates progress, speed, machines. If you see a building with straight, proportioned columns it's neoclassical; if it has shiny glass, art deco motifs flaunted like in a 1930s hotel, it's clearly deco. The detail that matters: neoclassical is minimalist on principle, art deco can never resist putting ornaments all over the place.