Classify political boundaries by origin and compare forms of government by how power is held and limited.
A state, in geography, is a politically organized territory with a permanent population, a defined territory, and a government recognized as sovereign. A nation is a group of people who share a common identity -- often language, history, or culture. When the two roughly line up, geographers call it a nation-state. In practice, most countries are multinational states, containing more than one nation or ethnic group within a single set of borders.
Boundaries between states have different origins. Physical (natural) boundaries follow a natural feature, such as a river or a mountain range. Geometric boundaries are straight lines, often drawn with a ruler rather than around any natural or cultural feature -- much of the US-Canada border and many colonial-era borders in Africa and the Middle East follow this pattern. Cultural (ethnographic) boundaries attempt to follow language or ethnic lines, though real cultural groups rarely sort as neatly as a border requires, which has historically caused conflict where the two do not match.
Governments vary in how power is held and limited, and geographers classify them by structure, not by whether the class agrees with them. In a democracy, citizens hold power directly or through elected representatives. In a monarchy, a hereditary ruler holds the position -- a constitutional monarchy limits the monarch's power under a constitution and elected government, while an absolute monarchy gives the monarch nearly unlimited authority. An authoritarian government concentrates power in a single leader or small group with limited political freedom or competition. A theocracy structures government authority around religious law or leadership -- again, a description of governing structure, not a judgment about the religion involved. Beyond individual states, supranational organizations like the United Nations, the European Union, and the African Union let countries cooperate on shared goals above the national level.
Mastery looks like: They can classify a boundary as physical, geometric, or cultural and classify a government's structure from a description of how its power is held and limited.
Common stumbles: Confusing a ceremonial monarch with genuine ruling power; treating government-type classification as a judgment of good/bad rather than a description of structure.