Bias acknowledgement: the following quote is by a Libertarian.
I find this passage (found here: Libertarianism versus other Political Perspectives) helpful in discerning the difference between the more recent American Liberalism and American Libertarianism (Classical Liberalism).
"In simplest terms the primary difference between libertarianism and other political philosophies involves beliefs about the amount of authority government should have over peoples' personal and business matters.
Liberals want government to focus on doing what is "good," including providing what is often referred to as "social justice." To do that, among other policies, liberals expect government to: a) tax corporations and "wealthy" and "high income" citizens heavily to pay for the social justice programs and b) regulate business and personal behavior to the extent necessary for social justice.
Liberals and conservatives both believe that government's mission is some combination of: a) making the world better, b) providing moral leadership, and c) protecting people from themselves. Of course conservatives and liberals tend to disagree about what is good and what is moral. And whether or not you agree with those objectives, you are forced to pay for them with your money and/or your liberty. Ironically you pay for liberal and conservative programs, rules, and regulations — with your money and your liberty.
Libertarians believe that goodness is voluntary, morality is personal, human nature cannot be legislated away, and only harm to others should be illegal.
And, though libertarians believe in limited government, as described in the U.S. Constitution, they do not want chaos. Libertarians recognize that government has a clear and critical mission: preserving and enhancing liberty. To achieve that goal government must: a) protect citizens from foreign enemies, b) arrest, try, and punish people that harm or endanger others, and c) make some judgment calls when peoples' liberties conflict." – James Eyer