The word "liberal" often confuses students as it can have two very different meanings. When one hears the word deployed in today's American political rhetoric, it signifies (sometimes disparagingly) someone who believes in big government, high taxes, is weak on defense policy, and is out of touch with traditional American values. Modern liberalism and modern conservatism are actually two separate branches grown from the tree of classical liberalism. An easy, if somewhat oversimplified, way of thinking about the difference is that the two variants are mirror images of each other.
Modern conservatives believe the government should refrain from excessive intervention in the economy (e.g., keep taxes and regulations of business low, restrain the growth of government welfare policies and public employment). The term "social conservative" is often used to describe those conservatives who believe government should actively promote social and moral, usually traditional, values and regulate immoral conduct. They are more likely to support prayer in school, and oppose abortion, same-sex marriage, and flag burning. The term "libertarian" is used to describe individuals who favor government non-interference in both economic and moral matters.
Modern liberals believe the government should actively intervene in the economy to correct market failures and promote fair outcomes (e.g., higher minimum wages, higher taxes on the wealthy, more regulations protecting worker safety and the environment). However, the government should refrain from interfering in an individual's social or moral choices (e.g., pro-choice, zealous advocacy of separating church and state, and less harsh penalties for "consensual crimes" such as smoking marijuana). Conservative and liberal are both ideal types. Many Americans fall somewhere between the two or appear to be closer to one or the other depending on the issue in question. As a generalization, however, Republicans are more likely to be conservatives and Democrats are more likely to be liberals.