By definition, "ancient" means everything before the Middle Ages, commonly understood as everything before 500 CE. So that includes ancient Egypt, Sumer, the Hittites, China, Greece and Rome, etc. On the other hand, when people mention "antiquity," they're generally talking about the period of ancient history circa 800 BCE to 500 CE. This is defined as the period coinciding with the Greco-Roman period, but it's important to note that there were other important developments going on in other parts of the world during this time as well.