A page in which I present a tendentious and simplistic account of modern Western political history.
There are four basic political traditions in the Western world: conservatism, classical liberalism, left liberalism and socialism. The present-day Right consists of conservatism and classical liberalism, while the Left comprises left liberalism and socialism.
Once upon a time in the 18th century
As recently as 250 years ago, there were no conservatives, liberals or socialists. The defining event in the emergence of modern political thought was the French Revolution of 1789.
The original conservatives were the opponents of the Revolution. They liked kings, aristocrats, churches, feudalism and a traditional agrarian form of society. The more moderate conservatives - like Edmund Burke - contented themselves with defending in general terms the virtues of continuity and tradition, and accepted that freedom had a valid role to play alongside stability and order. The more extreme conservatives - like Joseph de Maistre - were advocates of absolute monarchy, theocratic governance and severe punishments for anyone who stepped out of line. Moderate conservatives tended to be British and extreme conservatives tended to be French (although Burke was Irish and de Maistre was a Savoyard).
Their opponents were the liberals. They advocated a new form of society based on reason and liberty. They wanted to replace traditional monarchies with constitutions and parliaments. They also wanted individual nations to have the right to independence and self-determination. The conservatives thought that they were naive fools who were recklessly tearing up society by the roots. When the reign of terror began in France, followed by the rise of Napoleon, it looked like they might have a point.
At this point in time, it is the liberals who are in favour of small government and nationalism, while the conservatives oppose those things. Back in the 18th century, conservatives had no problem with the idea of a strong, coercive state, and they opposed attempts to break up traditional empires into modern nation-states.
Fast forward to the mid-19th century
Things are now starting to change.
Most of the 18th century liberals believed in the right to acquire and retain private property, but some of their more radical brethren had suggested that wealth, like political power, ought to be shared around more equally. By the middle of the 19th century, the industrial revolution is under way. An unprecedented amount of wealth is being created, but not much of it appears to be trickling down the social ladder. Some people are coming round to the idea that this newly created wealth ought to be redistributed, either by the state or by organised labour. These are the socialists.
The most famous socialist is Karl Marx, who thinks that the new capitalist economy is doomed because it carries within it the seeds of its own destruction. The workers, he says, will rise up and take control of the newly industrialised nations of Europe and America. Others on the Left - the anarchists - predict that this will just lead to a new and different type of state repression, and advocate abolishing the state altogether. Luckily, Marx is on hand to assure them that their fears are groundless.
On the Right, it has become clear that the pre-1789 world of the Throne and the Altar has gone for ever. The old French monarchy returned to power in 1814, but it did so on a reformed, constitutional basis, and it was overthrown and replaced with a still more liberal monarchy in 1830. The hardline conservative programme of restoring the old feudal order has begun to run out of steam - though the Catholic Church will carry on pushing it until Pope Pius IX dies in 1878.
Fast forward again to the end of the 19th century
By now, the liberal movement is showing signs of wear and tear. A split has opened up between classical liberals and left liberals. Classical liberals are sticking with the old programme of limited government, constitutionalism and property rights. Left liberals are arguing that the world has changed now, and that freedom doesn't just mean freedom from coercion by kings and priests: it means freedom from poverty, hunger and disease as well. This in turn entails government action, which is anathema to classical liberals. The left liberals don't want to overthrow capitalism altogether like the socialists do, but they do want to take the rough edges off it.
Meanwhile, things are kicking off in the socialist camp. Some socialists are still waiting for the revolution to come, but others want to work inside the system to implement more gradual change (much like the left liberals do). This split grows in the early 20th century and is broken wide open by the Russian Revolution of 1917. The radical socialists are now calling themselves communists, while the moderates become known as social democrats (a term which had previously meant something different, but don't worry about that). As is often the way on the Left, the two groups develop a cordial hatred for each other.
As if this wasn't enough, the violence and destruction wrought by World War I and the serious problems of the interwar period have created an opening for a new political movement. In the countries in which it takes root, this movement promises a national resurrection from decadence, brought about by a departure from the liberal constitutional tradition and a violent attack on the enemies of society. These guys reject both the traditional Right and the Left, but in practice they tend to hate socialists and liberals more than they hate conservatives, so they tend to be placed on the Right. They are known as fascists. They mostly disappear after they are annihilated on the battlefield in World War II by an unlikely alliance of conservatives, liberals and communists.
The political map has changed massively since the battle lines were first drawn in the 18th century. The classical liberals are now in alliance with their original adversaries, the conservatives, largely because they both now have shared enemies in the form of socialists and left liberals. Some people who have a particularly rigorous take on the classical liberal tradition are now calling themselves libertarians. In the United States, a distinctive form of American conservatism has taken shape that fuses elements of old-style conservatism and classical liberalism.
Conservatism now mostly means the moderate, pragmatic form of conservatism espoused by Burke. The extreme variant espoused by de Maistre is mostly obsolete in the West, though it still has some supporters, and it has some striking similarities to political Islamism. It is doubtful whether extreme conservatism can even be considered "conservative" any more, since those who still adhere to it are seeking to transform modern society rather than to conserve anything: a better term would be radical traditionalism.
On the Left, communism has been a lost cause since the Berlin Wall came down in 1990 and the Soviet Union collapsed in 1991. Socialism is looking a bit peaky too (in America, it never really took off at all, and "socialist" has become a term of abuse). The modern Western left largely comprises a pale pink combination of left liberalism and social democracy.
And finally - an oversimplified summary of the fundamental principles behind the West's various political traditions:
Socialism, communism - Equality (not only political and social, but also economic)
Classical liberalism, libertarianism - Freedom (political, social and economic); an approach to politics based on rationality
Left liberalism - A mixture of the above (i.e. equality, freedom and rationality), in different strengths
Conservatism - Pessimism about human rationality; preference for the established order
Radical traditionalism - Reconstructing society to conform to a prescriptive traditional order (e.g. Biblical, Koranic)
Fascism - Devotion to nation or race and aggression towards perceived enemies; rejection of liberal values (as above)