Final answer:
The Aztecs and Mayans are part of the New World as cultures of Mesoamerica, while the Greeks and Romans are part of the Old World encompassing Europe and adjacent regions.
Step-by-step explanation:
The societies of the Aztecs, Mayans (Maya), Greeks, and Romans are associated with different world zones. The Aztecs and Mayans are part of the New World, specifically the region known as Mesoamerica, which refers to Pre-Columbian cultures in Central America before the arrival of Europeans. On the other hand, the Greeks and Romans are part of the Old World, historically referring to the regions of Europe, Asia, and Africa. The Eastern World generally refers to Asia, while the Western World mostly refers to Europe and the Americas post-Columbian contact. Therefore, the Aztecs and Mayans fall under the new world classification, whereas Greeks and Romans fall under the old world classification.