The Maya, Toltic, Inca, and Aztec are four indigenous South and Mesoamerican cultures. Much of what they held in common was determined by natural resources- like the production of pottery and stone goods, or the raising of crops of maize and beans. Depending on the time period, extent of the civilization, and geographic location, there were some distinctive differences that set them apart.
The Maya civilization has its origins prior to 2000 BCE, but really crystallized and thrived between the third century BCE and the seventeenth century CE. Early on, society was sharply divided between the elite and lower classes. Over time, the population increased and so did the degree of stratification and specialization. Classes of farmers, soldiers, slaves, artisans, merchants, and nobles all served to maintain and reproduce society in support of a divine, hereditary king. The king's job was to negotiate the relationship between the people on Earth and the Gods.
Maya territory was widespread throughout the modern-day nations of Mexico, Guatemala, Belize, Honduras, and El Salvador. City-states primarily supported themselves but also established trade networks with each other to manage a surplus or dearth of specialty goods. Art made from wood, jade, and ceramics were common and might be traded. The Maya developed systems of writing mathematics, and astronomy, including a complex calendar.
The Toltec civilization is still a little bit mysterious to archaeologists. They are considered to have been influenced by, but separate from the greater Maya culture. They rose as a conquest-driven society, incorporating surrounding territories and instituting trade and some degree of cultural homogenization in these areas. Unfortunately, much of what we have learned from writing about the Toltecs is heavily bound up with mythology, so it can be hard to say what is true. We do know that they were a relatively short-lived society, thriving from about 900 to 1168 CE. They had a cultural narrative of a luxurious lifestyle and skilled potters and metallurgists, but archaeology does not support this claim. However, we know that they used systems of writing and medicine and traded obsidian with neighboring territories.
The Aztec civilization was centered in Northern Mesoamerica and experienced their peak between 1345 and 1521 CE. The empire was established through conquest but informally maintained through the installation of local rulers or alliances formed by marriage. Government was localized but involved tribute from all states to the central city of Tenochtitlan. Society was essentially organized into the nobility, peasantry, and slave classes. Different regions of the empire had specialties of production, like cloth, obsidian, or craft goods. These goods or a surplus of crops were used as tribute to the ruling class, and a commercial economy also involved trade of such goods or a monetized system using cacao beans. Music and poetry were highly valued by the Aztecs, and they also had a system of writing which may be studied from surviving ritual codices.
Between 1438 and 1533 CE, the Inca civilization thrived in what we now know as Peru, Bolivia, Columbia, and Ecuador. Territory was acquired through conquest or peaceful assimilation, and society was highly stratified and organized through an administrative system based on the number ten. An absolute king lived in the capital city of Cuzco, and below him was a nobility of ten families, then a lower nobility of ten more families, and so on. Local administration served to maintain a census and collect taxes (paid in goods,) which were then redistributed throughout the empire. The Inca had a refined and complex weaving culture, and even considered textiles to be of greater value than precious metals. They also crafted art from wood, ceramics, metal, and painted murals, all of which incorporated geometric motifs. Society was highly controlled by the government, so much so that people could not change their style of clothing without governmental approval.
As you can see, all relied on agriculture and systems of trade. Some societies employed systems of taxation or tribute to maintain the empire, but others were more loosely or locally governed. Perhaps the biggest difference between these cultures is the degree to which their society was stratified, specialized, and under control by a central power.