To make a very, very long story short and as vulgarised as possible.
Conservatism: A political philosophy that supports a system of class and a strong hierarchy where a series of greater rule over a series of lesser based on a longstanding tradition derived from history and a particular nation's culture. In the modern Western world, it's the idea that the members of the upper class, based on their wealth, should have a greater amount of power and authority on politics and culture than the lower classes. Deviation from traditionnal social norms is frowned upon as are any significant change to the economical system that set the hierarchy in place.
Liberalism: A political philosophy that support the idea of a lose hierarchy based on humanist, equalitarian and democratic ideals as developped during the late Middle Ages to today. In the moden Western World, it's the idea that all humans, no matter their ethnicity, sex, creed, sexual orientation and identity should have equal amount of power and authority on politics and culture. Deviation from social norms are accepted and often embraced as long as they do not threaten others safety. Open to cultural and economical changes as long as it leads toward greater freedom and equity.
Rightism/The Right: The political wing that trends toward conservatism. The more on the right the more conservative it gets, from "fiscal/progressive conservatives" down to reactionaries who want to return the world to a past state.
Leftism/The Left: The political wing that trends toward liberalism. The more on the right the more liberal it gets, from keynesian down to anarchists.
Capitalism: An economical doctrine that emphasis private property of the means of production, distribution and exchange and more specifically the idea that the amount of capital one has determines your wealth and the wealth of your nation.
Socialism: An economical doctrine that emphasis the idea that the means of production, distribution and exchange should be owned or regulated by the collectivity itself instead of individual actors.
Libertarianism: A political philosophy that combines the ideals of capitalism and liberalism to create a society in which individual freedom is maximised and all sense of collectivity is diluted as much as possible.
Fascism: A political philosophy that combines the ideals of conservatism and socialism to create a society in which individual freedom are reduced to a minimum for the benefit of an ruling elite class and a homogenous lower class. It's most simply described as military culture and chain of command applied to the entire society.
Communism: A political philosophy that combines ideals of liberalism and socialism to an extreme degree to create free and equal communities that live interdependantly and harmonuously.
Nation: A stable community of people formed on the basis of a shared language, culture, history, territory and/or ethnicity.
State: A nation(s) or territory considered as an organised political community under one government.
