For starters, a political ideology is the set of principles which guide and inform one's social, economic, and foreign policies. All the terms listed in the previous paragraph denote various political ideologies.
The following diagram will give us a frame of reference to talk about these terms:
Libertarianism: This is the view that the role of government should be limited largely to protecting our borders and constitutional rights. Libertarians believe that government should, except to protect citizens, stay out of our personal lives and out of the marketplace. They are also very reluctant to get involved in foreign conflicts. Senator Rand Paul who recently withdrew from the race for the Republican nomination for president, is perhaps the most well-known contemporary libertarian politician. Ayn Rand (who wrote Atlas Shrugged and for whom Rand Paul is named) is the most well-known libertarian writer.
Conservatism: Conservatives tend to be libertarians, but see a somewhat more expansive role for government. The emphasis among conservatives is on preserving traditional values and the Constitution and also upon diffusing governmental authority from the central, federal government and giving it back to the states and localities. They're reluctant to change unless it can be shown that the change is both necessary and has a good chance of improving the problem the change is supposed to solve.
Conservatives take a strict view of the Constitution, interpreting it to mean pretty much precisely what it says, and oppose attempts to alter it by judicial fiat. They also oppose government interference in the market by over-regulation and oppose high tax rates as being counter-productive. They strongly oppose illegal immigration and believe in a strong national defense, but, though more willing to use force abroad when our interests can be shown to be threatened, are nevertheless leery of foreign adventures. Ted Cruz is perhaps the most well-known contemporary conservative politician, and William F. Buckley is the most well-known conservative writer.
Moderates: Moderates tend to be conservative on some issues and liberal on others. They see themselves as pragmatists, willing to do whatever works to make things better. They see themselves as non-ideological (although their opponents often see them as unprincipled). President George W. Bush was a moderate politician and New York Times columnist David Brooks would be an example of a moderate writer.
Liberalism: Liberals see a more expansive role for government. They take a loose view of the Constitution, interpreting it according to what they think the founders would say if they wrote the document today. They tend to think that traditional values shackle us to the past and that modern times and problems require us to throw off those shackles. They agree with libertarians that government should stay out of our personal lives, but they believe that government must regulate business and tax the rich and middle classes to subsidize the poor. They tend to hold a very strong faith in the power of government to solve our problems, a faith that conservatives and libertarians think is entirely unwarranted by experience. President Bill Clinton might be an example of a liberal politician.
Progressivism: Progressivism can be thought of as hyper-caffeinated liberalism. Most prominent members of today's Democratic party are progressives as are many in the mainstream media and on cable networks like MSNBC. Progressives tend to see the Constitution as an obstacle to progress. Whereas conservatives view the Constitution as a document which protects individual rights, progressives see it as an archaic limitation on the ability of government to promote social and economic justice. They tend to be indifferent to, or even disdainful of, traditional values and institutions such as marriage, family, and religion.
Progressives are essentially socialists who are reluctant, for whatever reason, to call themselves that. A humorous depiction of progressivism can be found here. President Barack Obama and candidate Hillary Clinton are progressives.
Socialism: As stated in the previous paragraph, socialists are progressives by another name. Both progressives and socialists desire that power be located in a strong central government (they're sometimes for this reason referred to by their opponents as "statists.") and both wish for government to be involved in our lives "from cradle to the grave" (see this ad which ran in the last presidential campaign). They favor very high tax rates by which they hope to reduce the disparity in income between rich and poor. Perhaps one difference between socialists and progressives is that though both would allow corporations and banks to be privately owned, socialists would impose more governmental control over these institutions than progressives might. Presidential candidate Bernie Sanders is an example of a contemporary socialist.
Fascism: Typically fascism is considered an ideology of the right, but this is a mistake. Fascism, like communism, is a form of totalitarian socialism. Indeed, the German Nazis as well as the Italian fascists of the 1930s were socialists (The Nazi party was the National Socialist Party). Fascism is socialist in that fascists permit private ownership of property and businesses, but the state has ultimate control over them. Fascism is usually militaristic, nationalistic, and xenophobic. It is totalitarian in that there is usually only one party, and citizens have few rights. There is no right to dissent or free speech, and fascists are prone to the use of violence to suppress those who do not conform. Those on the far left on campus who shout down speakers and professors whose message they don't like are adopting fascistic methods.
Communism: Like fascism, communism is totalitarian and socialist, but it's a more extreme socialism. Under communism there is no private ownership. The state owns everything. Moreover, communism differs from fascism in that it is internationalist rather than nationalist, and it doesn't promote a militaristic culture, although it certainly doesn't shy from the use of military force and violence to further its goals. Like fascism, however, communism does not permit free speech, and those who dissent are executed or cruelly imprisoned.
Few completely communist nations remain today though throughout much of the twentieth century the Soviet Union, Eastern Europe, China, Cuba and many other Asian and African states were all communist. Today North Korea is probably the only truly communist nation. Scarcely any contemporary politicians would admit to being communists though some of President Obama's close associates and friends over the years, such as Bill Ayers and his wife, Bernardine Dohrn, Van Jones, and mentor Frank Marshall Davis are, or were, all communists.
I hope this rather cursory treatment will be helpful as you seek to make sense of what the various pundits and candidates jockeying for their party's nomination are saying.
