To my understanding, modern terminology such as infantry, cavalry and artillery, and especially light vs heavy and roles like skirmishers etc. generally originate from 17-18th century European efforts at military reforms and standardisation.
However, Renaissance-era terminology aren't designed with ancient history in mind. How did the ancients categorise contemporary troop types and battlefield roles when debating about military matters? Some basic categories are universal like foot vs mounted troops. There are also known historical categories, such as chariot vs horse troops from the earliest Sumerian days. Others still are open questions based on my own limited knowledge: Were ancient melee cavalry also divided into two roles (light and heavy) just like in modern terms, or were they differently categorised, perhaps by the roles suited to different levels of armour protection - no armour, partial armour, full catacphract, and giant elephants?
When identifying different battlefield roles and the categories of soldiers that fill them, in what way are the ancient ways of describing contemporary armies similar and different to the modern way of identifying the same ancient armies? In this question, "ancient" is defined as encompassing all time periods before the Renaissance, during which modern terminology originated. Up till the systematic adoption of gunpowder, warfare had not seen revolutionary changes since the domestication of beasts of war.
While the focus is on the world stretching between Europe and the Near East, any info on Asia would be a worthy addition to an answer as well.
Edit: Perhaps I should clarify that I don't really need a detailed treatment of every civilisation (that is just a bonus if it is feasibly achievable). All I want to know is how much the ancients and us think alike - a rather simple generic answer, as long as it is supported with evidence from ancient military thinking/theories. Exactly how they differ from us, or how the ancient Assyrians, Persians, Romans, Byzantines, Ottomans, Indians, Chinese, Mongols etc. view the conduct of war is good-to-know if available, but not necessary. What I describe above are just examples of how things may be done differently in the past to prove my point.