What is the name of the state system of Athens, what is the name of the state system of Sparta, and why they call it that.

The state system in Athens was called democracy, since any citizen of this city could take part in political life.

The state system in Sparta was called the oligarchy. There, all state issues were decided by the council of elders, which consisted of the most influential (and therefore the richest) citizens. The kings, although they existed, were essentially military leaders and did not have power in governing the state. the popular assembly did not play a significant role: it only elected officials and approved the decisions they made.